Specs updated, thanks Centaur! Just a few updates:
Since my post I reinstalled Windows 7, and it did not fix the issue. I still received BSoD just as frequently, and at one point I received 2 in a row, before windows could even start up again.
At this point I had the idea to remove my video card and boot up using the integrated graphics in my i3. The video output on my motherboard worked and it started up, but once it got to the "Windows 7 is starting" screen the output shut off. As in, the computer kept running but my monitor wasn't receiving any signal. Confused, I reseated my video card to make sure that still worked. It did, and funnily enough it seemed to fix my problem for a time. At least, for several days I didn't have a crash. It eventually crashed again, but every time I've had two crashes near each other I've reseated my GPU, and it has seemed to help. I have no idea what to make of this, other than maybe my PCI-e lane is a little off and begins to lose connection if my card gets wiggled around?
Anyway, sorry for the wall of text, but I have a new round of minidumps for you, since my reinstall. I've been checking BlueScreenView every time, and it always mentions ntoskrnl.exe and another file, but the second one seems to change a lot.
Thanks so much for taking a look!