I am currently running Kubuntu 18.04, but these issues affect other distributions as well. I have tried multiple nvidia drivers, and none of them work properly. I have a laptop with a soldered GPU (Quadro FX 1800M), no integrated graphics, and no support for integrated graphics, so I have to keep using that GPU unless I buy a whole new system, which I really don't want to do.

With the nvidia-340 package (which I will refer to as the proprietary driver), the newest proprietary driver that supports my GPU, there are multiple issues, none of which happen with the free driver:
1. The switch user dialog has a button to start a new session. On the nouveau drivers, this creates a new session and switches to it, but keeps the old session. I can switch between both sessions with the switch user dialog. I am pretty sure that is the intended behavior, and it is the behavior I want. On the proprietary drivers, the add session button ends the current session and starts a new one. I think it restarts the entire X server. This is extremely irritating (I share this laptop with my brother) and can possibly result in lost data if someone is rushed or isn't careful.
2. Is it possible to remove or replace the Nvidia logo that appears every time I boot my computer, log out, or log in? I hate Nvidia because of their shitty drivers (my next laptop will have Intel integrated graphics) and don't want to have my computing experience ruined by having to look at their logo.
3. Whenever I wake up from sleep, some areas of certain windows get visual artifacts on them (this happens on all DEs and distros as well) that disappear if I change the size of the window or otherwise make it re-render. Here is a screenshot showing an example of it happening in VS Code compared to what it is supposed to look like.
4. Waking after sleep will sometimes work perfectly, but will sometimes (especially if my system is heavily loaded) take a stupidly long time (5-10 minutes) to display the lock screen. It is often faster to kill X, log in again, and re-open all my stuff than it is to wait for that. In fact, it is often faster to shut down the computer completely and turn it back on again later than it is to wait for that. I have to suspend and wake up a lot, so this is unacceptable.
5. How do I change the boot animation or replace it with a verbose boot? The nvidia drivers replaced the nice-looking default boot animation with an ugly and low resolution one that, like their logo, I also don't want to look at.
6. If my system is heavily loaded, applications will sometimes appear to freeze and become hard to switch out of, then crash and bring down the entire graphical session with them. I have to log in and re-open all of my graphical applications every time this happens. This is also unacceptable.
7. The GPU performance is terrible, usually slightly worse or barely better than not using GPU acceleration at all. 60fps Youtube videos stutter, especially if played at 2x speed. UI animations on websites stutter. Scrolling usually stutters. Almost anything more graphically intensive than plain text and images is annoying to use.
8. The system runs about 10-15°C/18-27°F hotter under similar conditions than it does with the other drivers, which suggests that it is using a lot of power.

With the nouveau driver, all of those issues are fixed, but it often causes my entire system to crash without any warning. I think it is causing kernel panics because the screen stops updating, my laptop disconnects from the network, the hard drive light stops flashing, and the system does not respond to REISUB (it normally does) and therefore can only be recovered by holding the power button or removing the AC adapter and battery. I actually need my system to work, so this is completely unacceptable and is the reason why I am currently using the other driver.

Someone on here told me that if I uninstall both drivers, Xorg will fall back on something called the modesetting driver. Uninstalling both drivers caused the system to behave mostly as if it was on the nouveau drivers, including the random kernel panics. The only difference was that I could not use KDE's desktop effects and some other GPU dependent things.

Is there a way to fix all of the issues with any of these drivers? I think the best option would be to fix the kernel panics with the nouveau driver, but I don't even know where to begin with any of this.

The Nouveau DDX driver is old technology. The Modesetting DDX driver is much newer technology, provided by the X server package instead of as a separate DDX driver package. For most people who find their GPU is no longer supported by a proprietary driver, the Modesetting is more likely the best choice available. Testing is the only way to tell which is preferable. Please post output from:and pastebinit /var/log/Xorg.0.log so that we might spot some problem that something might be done about.

Regarding boot issues, and possibly other issues, Plymouth might be playing role that can be eliminated by uninstalling it. To test whether it helps, at the Grub boot menu, strike the e key, move the cursor to the end of the (possibly wrapped) linux line, remove splash=silent, optionally remove quiet, and append plymouth.enable=0, then proceed with boot. The result will be a lot of text messages, and hopefully also some graphics mode improvement. If success, either uninstall Plymouth, or reconfigure your bootloader via /etc/default/grub's GRUB_CMDLINE_LINUX_DEFAULT= and GRUB_CMDLINE_LINUX= lines to match the test, then update Grub.

inxi -Gxx gives me:
/var/log/Xorg.0.log is at https://pastebin.com/0eGS49bB.

I believe I have already tried the modesetting DDX driver by removing both the nvidia-340 and nouveau packages. It resulted in the same behavior as nouveau, except with some GPU dependent stuff not working. Was I doing it right? I don't think I'll bother attempting to fix the boot animation if it is going to involve lots of troubleshooting and editing config files.

Having Plymouth removed could impact other things. It's worth trying the cmdline test to see. openSUSE users using proprietary NVidia drivers are instructed to remove Plymouth entirely. Plymouth removal might be the only thing you need to do to reach nirvana.

The Xorg.0.log I was expecting was from using nouveau DDX or modesetting DDX. Yours with NVidia tells me nothing about whatever might be malfunctioning or missing when using the FOSS DDXes. Another would be moot if Plymouth removal works.

Well, I was having these exact issues on Debian too, which does not have Plymouth AFAIK. Should I still attempt Plymouth removal? If so, should I switch to a FOSS DDX before doing that?

Debian has Plymouth on the mirrors, so it might have been installed. Go ahead and try the plymouth.enable=0 on kernel cmdline test, first.

I would not.

"Disabling" plymouth just made my system sit there with a black screen and the hard drive light flashing for almost a minute, then boot normally with Plymouth enabled. Otherwise, nothing changed. Also, I'm going to bed and should be able to continue tomorrow.

None of my 18.04 installations have Plymouth installed, so I can't really test if how to temporarily disable it works as in the past. You might try noplymouth instead of plymouth.enable=0 instead. Make sure you have a space between either and whatever character ends the last parameter on the linux line.

It turns out that you need to remove "splash" from the Linux command line to disable plymouth, and "quiet" to get a verbose boot. I'll leave it that way because I want that anyways. This fixes number 5. The performance and temperatures also seem more reasonable now, but I haven't had a chance to do a proper test yet. I'm still on nvidia-340.

1, 2, and 3 are definitely not fixed. I still have those issues.

No testing has been done for 4 and 6 yet.

5 is definitely fixed.

7 and 8 seem mostly fixed, but I need to do more testing.

Does replying bump this to the top? mrmazda suggested disabling Plymouth on the proprietary drivers, which was helpful but did not fix everything. Here is what still needs to be fixed:
1. The switch user dialog has a button to start a new session. On the FOSS drivers, this creates a new session and switches to it, but keeps the old session. I can switch between both sessions with the switch user dialog. I am pretty sure that is the intended behavior, and it is the behavior I want. On the proprietary drivers, the add session button ends the current session and starts a new one. I think it restarts the entire X server. This is extremely irritating (I share this laptop with my brother) and can possibly result in lost data if someone is rushed or isn't careful.
2. Is it possible to remove or replace the Nvidia logo that appears every time I boot my computer, log out, or log in? I don't want to have to see that.
3. Whenever I wake up from sleep, some areas of certain windows get visual artifacts on them (this happens on all DEs and distros as well) that disappear if I change the size of the window or otherwise make it re-render. Here is a screenshot showing an example of it happening in VS Code compared to what it is supposed to look like.
4. Waking after sleep will sometimes work perfectly, but will sometimes (especially if my system is heavily loaded) take a stupidly long time (5-10 minutes) to display the lock screen. It is often faster to kill X, log in again, and re-open all my stuff than it is to wait for that. In fact, it is often faster to shut down the computer completely and turn it back on again later than it is to wait for that. I have to suspend and wake up a lot, so this is unacceptable. Disabling Plymouth makes this happen a little more infrequently and makes it a bit easier to recover from it with the console, but it is still annoying.
5. If my system is heavily loaded, applications will sometimes appear to freeze and become hard to switch out of, then crash and bring down the entire graphical session with them. I have to log in and re-open all of my graphical applications every time this happens. This is also unacceptable. Disabling Plymouth seems to make them stop bringing down the entire graphical session when they crash.
6. The GPU performance is terrible, usually slightly worse or barely better than not using GPU acceleration at all. YouTube videos stutter, especially if played at 2x speed. UI animations on websites stutter. Scrolling usually stutters. Almost anything more graphically intensive than plain text and images is annoying to use. Disabling Plymouth makes it start out with reasonable performance but within a few hours it is bad again.
7. The system runs about 10-15°C/18-27°F hotter under similar conditions than it does with the FOSS drivers, which suggests that it is using a lot of power. Disabling Plymouth seems to make it significantly cooler, but not the full 10-15°C cooler.

The FOSS drivers (both nouveau and modesetting, as far as I can tell) don't have any of those issues, but will randomly kernel panic the system, which is even more unacceptable than the issues from the proprietary drivers.

Perhaps this will be considered trolling, but if I have problems with NVidia hardware, I just throw it away. I'm certainly never in the market for laptops with NVidia cards, used or otherwise.

Certainly there are circumstances (professional) where that isn't an option-- none that apply to me.

Good for you. I am a 16 year old with very little of his own income, and I want to continue to use this laptop as long as possible. When I replace it, I want to get something high end, repairable, and macgyverable so I can use it for a long time. I probably won't be able to get a real job until this summer and this laptop has a soldered Nvidia card and no integrated graphics, so I have to keep using the Nvidia card, at the very least until then. Of course, I still want to get at least two to six more years out of this laptop if the Nvidia graphics can be fixed.

If I have a spare mPCIe slot (or at least am willing to remove my Wi-Fi card and use USB Wi-Fi or Ethernet), does this mean I can get an adapter to connect to a cheap GPU and connect that to a cheap monitor, avoiding the need to use the Nvidia card AND the need to buy a new machine, assuming I hack their power supplies to run off my laptop's 12 volt rail? And of course make an external battery pack (or a few) to improve the battery life and then duct tape them all together so it still looks like a laptop? Would that cost less than buying a new machine?

This points to probable hardware trouble. I suggest tomorrow night before bed starting memtest86 7.x (not memtest86+), then not touching it again until Sunday AM (any period of >24 hours actually). If no memtest errors, put a different HD in it and install Windows. If Windows crashes too, either give up, or open it up and clean it thoroughly. If Windows does not crash, try a non-Debian based distro, as 18.04 is. Absent hardware trouble, you should have it working acceptably by now. What brand and model is this 9 or 10 year old laptop? When did you acquire it? When did it last work acceptably, using what OS?

This laptop is a Dell Precision M4500 that I got in either 2014 or 2015. It was refurbished, and I think (I may have to check) it has a new hard drive, new RAM, and a new battery. I abandoned Windows 7 in 2016 because it was too slow and was having too much trouble with internet drivers. It would not connect to a wired network and would not recognize my Wi-Fi card at all (on Windows). Graphics drivers on Linux never worked quite right, but the machine is still overall better on Linux than it was on Windows. I've been having the exact same issues for years and just decided to try to fix them now. If it was a hardware issue, I would think it would get worse over time. I don't have a spare hard drive and don't really want to download over 4 gigabytes, but which distros do you recommend trying? I think I can memtest it either overnight tonight or over the weekend. Any reason why I should use MemTest86 and not MemTest86+?