Possibly damaged cpu / ram?

[AncientPC]

I'm trying to fix my roommate's comp, and here are the symptoms:
01) with no warning computer powers down and restarts
02) sometimes starting up cpu / memory intensive programs computer stops, mouse freezes, and hdd light stays on constantly
03) these errors started popping up after he ran NU 2001's Speed Disk.

Possible reasons for the errors:
- bad ram causing computer to reboot?
- bad cpu?
- power supply is die'ing?
- I'm sure it's not a connection problem because his computer is never moved . . .
- I remember someone before stating that they were having similar problems after running NU 2001's speed disk

I've tried:
- rerunning speed disk (comp never crashes)
- disk doctor incluiding standard surface scan (no errors, never crashes either)
- NU system check up
- mind you, all this happens after I boot up, log-in, and clear all unnecessary programs through task manager (using a Win98SE)
- never crashes in safe mode either

My roommate's computer is a Micron PC, so I may just ask him to take it back into the shop to have them look at it . . .