Lock ups are always a bitch to test. Download a linux boot disk like Knoppix and run it for a day or two if you can. If it still locks up, you’re looking at a hardware issue, either overheating (which it doesnt sound like) or an electrical short. And for fucks sake, if the PC’s sitting directly on carpet, slap yourself and then place it a little higher on something. Sooo many people I know had PC problems until they got their PC off of the carpet.
If it doesn’t lock up, then it’s a software issue causing (and hardware drivers falls in this too). You can either look through the system’s event viewer to see when exactly it died and if there are any common problems when it locks, or just wipe it and reinstall Windows and everything.