I replaced the motherboard and that fixed the problem.
A few days ago, I fell asleep with my computer on, and it was making a lot of fan noise throughout the night. When I got up and turned it off and on, it started having this problem, with multi-colored horizontal lines across the screen (pictured). After it logs on, it also has had various BSOD's within 10 secs to a minute including "page fault in nonpaged area," "bad pool caller," or "memory management." After one of the BSOD's the computer wouldn't boot anymore, so I had to reinstall Windows (all my stuff is backed up). When I boot into safe mode everything is fine. And if I uninstall or disable the display adapter, everything is fine (despite not being able to use the video card).
I tried several things: Installing new display drivers, dusting out the machine and video card, buying and trying out a new video card, reinstalling the chipset drivers. Nothing has worked so far- it still has the same problem.
This leads me to suspect that it might be a motherboard problem, but I really don't know.
Here are my specs:
Windows 7, 64bit
Processor: AMD Phenom II x6 1090T Processor (6 CPUs), ~3.2GHz
RAM: 8GB DDR3
Motherboard: ASUS M5A97
Video Card: I was using GeForce GTX 560Ti, and I just installed a GeForce GT 740 FTW that I'll probably return since it didn't fix the issue.