Power keeps shutting off

I have a strange dilemma going on with a cheapo EMachine Computer. It's a T2792 with a 2.8 Celeron processor and I have updated the power supply to an UltraV 500 watt unit. My problem is, it will shut the power off to the motherboard after running for a short time (seems to still have power in the PSU as the fan is still running on the PSU but the processor fan shuts off). I then turn the power switch off of the power supply and back on and the computer will power back up again and then repeat the shutting off problem. First I was thinking power supply, but it checked out to be okay (very basic test) and then I was thinking processor or motherboard, but I started it up into safe mode and it seems to run just fine and doesn't shut off. It seems then that power supply is indeed okay and that the processor and motherboard are okay, except for maybe one of the on board components is causing it such as the on board video, modem etc.? Any areas to look at and how should I go about trouble shooting and eliminating things until it will stay running?

Thanks

Id be incline to agree... The PSU sounds like its the main fault... have you got another one to test with?

How about some sort of power management setting that turns off the pc after a while? The OP mentions that it doesn't happen when he boots into safe mode.