p.s. just out of sheer curiosity, what is the make/model of your modem?

Just to make sure there are no misunderstandings, I am not expecting my Internet connecting to operate at Gigabit speed, just "normal speed" which for me is about 40 Mbps and I'm okay with that. I am sorry if I am using terms incorrectly, I don't know much about networking. For about two weeks the Debian minimal install was accessing the Internet at a tenth or less of the speed it normally was. On the same machine with the same NIC, Internet access speeds where normal when using the Debian install environment and for some reason also the minimal Debian install after a desktop environment was installed. This all stayed very consistent for about two weeks. Today is the first day that the Debian minimal install has been accessing the Internet at normal speeds.

As for the maximum speed of my switch (btw, I'm not complaining about either my LAN speeds or my Internet speeds now), my router (WNDR4300) advertises "Gigabit Ethernet" -- this is why I was wondering if the whole 100 Mbps thing is correct.

Edit: Ehh! I meant to say this in post #8:
"I've install lxde-desktop from the Internet hundreds of times, it rarely takes over 10 minutes or even 5 minutes. The fact that it was taking over an hour shows that ISP speed is not the issue. When the NIC is working right, my download speeds are around 3.6 to 4 megabytes (not megabits!) per second, but it was around 300 kilobytes per second!"

Edit:
Hmm... My NIC is connect to my router, and my router is connect to my cable modem.

I never thought about the modem speed (duh!) just the NIC, cable and router speeds.
Modem: Cisco DPC3008 (That's all it said on the modem)
Router: WNDR4300

did you try going to speedtest.net
it seems unlikely to me that your card is failing

Speed test gives me 31.66 Mbps down, 4.30 Mbps up and a ping of 13 ms (all good as far as I'm concerned), though as I said, the Internet speed is miraculously acting normal again.

I was never concerned that the NIC was failing, it also download things fast from the Debian installer environment, but in a minimal Debian install, download speeds would be very very slow until I installed a desktop environment (very odd). From the Debian installer environment downloading LXDE took under ten minutes, but from a minimal Debian install -- over an hour. This has now fixed its self today and I don't know why considering that the problem was consistent for two weeks.

hmm, still unlikely the problem was your nic, more than likely something outside of your computer (cable lines are susceptible to noise and interference as well for instance). Next time you see that i would look at the web interface on your cable router, it should show connection statistics such as noise to signal ratio, etc..

Hmm... okay I'll go with that for now. I still find it odd that the problem only occurred in the minimal install but I guess it could be coincidence, though two weeks is a long time to stay consistent (what would be causing all that interference for so long? And why did it only effect that NIC and not the NIC of the other computers). Anyways, the Internet is working fine now but in the event that it starts acting stupid again, how should I interpret the router's statistics? Here's what it shows:
https://cdn.anonfiles.com/1404021579841.png

Given that interference is a problem, how should interference effect the values of those fields? Or does the router give an insufficient amount of statistical information to tell if interference is a problem, especially interference that only effect one NIC as it lumps all the LAN together?

hmm if that's the case i'd also try checking the cable between your computer and your router, sometimes a loose wire can cause problems as well, and is probably more likely than a bad nic, but who knows, maybe a driver issue.

A loose wire is probably the most likely culprit, with all four Ethernet ports occupied, they are all uncomfortably close to each other and the sides of each of the connectors' shielding rub against each other. If I unplug a cable and plug it back in, it can be very difficult to get it back in because the two cables on its sides are so close. I'll make sure all cables are all the way in right now.

Now that I am thinking of it, the cable that connects to the offending NIC does have the fattest head shielding (I have no idea why it is so fat), and it looks like pressure from the cables beside it could slightly push it out a little.

Until further issues, I declare the loose cables the cause of my troubles (though it's still odd that I only had issues in the minimal Debian environment [could be driver that for some reason the Installer environment and LXDE have] but it's working now so whatever .