Assuming you are using 2000 or XP the system will tell you what caused a crash. You have to turn off auto restart under power management in the bios.
Once autorestart is off, the system will pop up a nice blue screen (affectionately called the BSOD) with, maybe, some usable information on it.
Exceptions to getting the info screen will be if the problem is with the power supply or the processor going mind dead.
For power supply trouble shooting you need another power supply to try.
The porcessor may show high temperatures if it is the troublesome part. Check it in bios as you reboot (hit del and look under advanced in most bioses to get cpu and system temps). Make sure system is under 45 deg C and CPU is under 65 deg C. These are not normal temps, but rather the high end of where you will have stable operation. Normals should be under 38/58 under heavy usage (gaming, etc.).
I think RAM failures will give you a message on the BSOD. If not and you have, or can get, a second stick try them one at a time.