It sounds like a hardware problem, aksuzbero, either memory, graphics, hard drive or power supply. To help narrow it down,
1. Were you getting any error messages before it crashed,?
2. Were there any strange noises coming from inside the tower?
3. How many sticks of RAM are installed?
4. Was the display okay before the crashes?
5. Have you carefully cleaned out the inside of the tower, clearing any fluff from the fans and vents?
Is it possible that you could install the hard drive in another computer, to check the hard drive and to back up any important files you have on it?
You say you tried reinstalling Windows, what type of disk do you have, a manufacturer's restore disk or a full XP disk?