Odd Power Problem

I have a HP Pavilion Slimline that seems to be having some sort of power issue. It's really weird. After about 1-5 minutes the entire system will lose power and shut down, but its power light stays on! Fans do not turn, and no USB devices receive power, but the power light stays on until the system is unplugged or the power button is held down.

Windows doesn't seem to be the problem. It has happened when in the BIOS, BIOS boot menu, Windows boot menu, and Windows. The system is always quite cool to the touch as well so it's not shutting down due to overheating.

The only thing I can think of is that something could be wrong with the PSU. What do you think?

 

Do you have a spare power supply to test the system with?

If not, and only if you feel comfortable and will not void any warranty you may have left, open the case and unplug everything from the power supply apart from the motherboard and any graphics cards that require dedicated power. Then power up, go into the BIOS, and see if it shuts down or not again.