This computer has a random reboot problem about 2 or 3x a month. Most recently, the monitor went black for 1-2 seconds, then Windows reappeared and everything was frozen. Other times it's random reboots without a BSOD.
Could be a PSU issue but I'm also experiencing regular Firefox crashes. A post on the Mozilla forums suggests my RAM might be defective. I just bought this RAM in the last 12-14 months.
Did you run memtest? You can also run Windows Memory Diag if you have Windows 7? That will let you determine if you're looking at a memory problem, though with memory problems, they seem to occur more than 1-3 times a month. You'd be seeing things 1-3 times+ every time you try to use it if you have bad memory.
First thing I thought when I read your post was power supply. But try the memory checks and let us know.