Alright, this might be a mouthful, but please bear with me.

On my home PC my HDD died and I decided to install Linux Mint 18.2 on a fresh one as I have played around with Mint before. I put the ISO on a thumbdrive and had no issues with installation. However after the installation was complete I clicked on wireless networks, and it showed "Belkin", but when I clicked on it to connect the wheel just spun like it was attempting to connect and then nothing happened. After a full day of toying with it and not being able to connect to the internet I threw my hands up in defeat and thought maybe I got a bad ISO or something, so I took my thumbdrive and put an ISO for Mint 17.1.

I installed 17.1 with no problems, and now I have no issues with connecting to Belkin. In fact I'm on it right now typing this message out. However the entire OS seems buggy as I can't get Wine to work properly, and other applications are not working well either. Well alright, I thought maybe it was just 18.2, so I tried Unbuntu 17.10. Same issue as before, I can see my wireless network but it just won't allow me to connect to it.

Then I attempted Zorin, but this time before installing it I played around with it while it was still on my thumbdrive. Perfection, no issues, was able to connect to Belkin and was able to logon to Chromium. So I installed it, and after that I tried to connect to Belkin it was the same exact issue again. I can physically see the network, I can click on it and go into settings, but it just won't connect to it. So now I'm back on Mint 17.1 and I connect to my network with no problem, I'm just having issues with applications which makes me want to try a different distro.

I'm pretty new at this, so I'm sorry if my post is long-winded, I just wanted to stress that I've tried multiple things and read multiple things for about two weeks before asking. My wireless works fine with 17.1, but only with 17.1. It also works with Zorin as long as I'm using it from the thumbdrive, but after installation it has the same issue. The other two nothing.

I'm sorry I didn't provide all the information I could, let me know what you need to answer, or should I just give up?

That looks to me like a software (possibly firmware) issue. Clearly the Zorin installation disk contains what is necessary to make the device work but it's not being installed. Please don't give up! This kind of problem is usually soluble if you work systematically.

First boot your Zorin disc and confirm that the card works. Then use the dmesg command to list the kernel's message buffer and see how the kernel has handled the device (it should be near the end). Now do the same with your installed Zorin. With any luck, you will be able to see a difference in the two outputs which will give you some guidance on what is going wrong.

You could try the same with Mint 17 and Mint 18.

When you installed Mint 18, did you select the option to install 3rd party codecs and drivers?

To troubleshoot the problem you need to know the chipset of your wireless card. To do that run:
It's probably a Broadcom card and they're known to be problematic. I've had them work with one kernel and break with an updated kernel.

The software that is usually involved here is called the wpa2 supplicant. Is that installed?

What happens when you attempt to connect? Anything in /var/log/syslog?

Just a note on firmware which you may find useful. Some proprietary wifi drivers include code that has to be loaded into the card's onboard memory before that card will function. The Linux kernel's version of the driver can perform this operation too but only if the file is available. What normally happens is that the main driver is stored as a module, which the kernel loads when it detects the hardware. Then the driver tells the kernel that such-and-such a firmware file is needed. The kernel looks for it in /lib/firmware. If it isn't there, the kernel will complain. If your installation disc contains the relevant file and your installed version doesn't, the solution could be something as simple as copying it over.

Yes, that's also a possibility. The output of dmesg should show whether this is a wpa error or a more basic one involving firmware (in which case the interface won't even come up). ifconfig should show this too. If the interface is up, it's a wpa problem.