Had a random reboot problem a while back. At first it was just when the game was on-line. Then anytime I use a video program (played a DVD, AH film or used a media player).
I looked for loose wires, tested power supply, cleaned hardware and software and added a fan as the vid card doesn't have one.
On a trip to Circuit City I went ahead and bought another 512 of RAM to get to 1 Gig. It improved reformance but not the reboots.
Almost as an after thought I removed the factory 512 and moved the new one over. The reboots stoped. Some of the chips on the old stick looked like the plastic had been exposed to heat where they meet the card. Kind of a dried out flat black with a ruff texture.
Needless to say I was back in town getting a match for the new stick of RAM.
If you can borrow some RAM that is compatible you may want to check this out, but only as a last or near to last resort. There are plenty of other things that can cause random reboot including a short in your joystick.(been there too).