There are a few places you can look when random crashing starts happening. This is on my mind right now, 'cause I'm getting random blue screen of deaths (BSOD). RAM can be wonky. To test the RAM, download an appropriate version of memtest86 (I have no floppy drive, so I downloaded a version that can boot from CD). Run it for 24 hours. If the RAM is bad, you'll know.

Next up would be the motherboard or the CPU. I know of no good way to test them, so if any orgah has a CPU test utility, please help a brother out.