Update: I did take it apart to get to the CPU yesterday. I'm hoping this was all a heat issue. I put WAY too much thermal paste on the die when I put the machine together, so I scraped a bunch off and put the thing back together. I'd run some program called Speedfan before and after the procedure, and the temps went from 50C to about 34C. Afterwards I wasn't able to get the machine to crash, but that's this computer's MO. It waits until I'm gone and then five days later my wife tells me her mom's computer crashed on her ten times in one night. I'll post again in a week if it's stable.

Is 50C enough to cause this level of problems? I know it's high, but it doesn't seem catastrophically high.