To determine if it is a hardware or software issue, try booting from a bootable floppy disk or CD.
If it still has problems, or dies after 15 minutes, then you have a hardware problem.
Check your CPU, power supply, and other cooling fans.
A fan failure is often the cause of short run times.
The next simplest piece of hardware to deal with is the Power supply.
I would want to have at least a 300 watt, if not a 400 watt supply in this PC.
Beyond the above you should go through the PC step by step and eliminate hardware and software.
I normally back up to aminimum configuration (CPU, RAM, Video) and see if that works, then add devices back in one at a time.
If a minimum configuration does not work, I swap hardware 1 piece ata time until I identify the culprit.
Chas