the symptoms mentioned could be a few things...
1.
PSU
2.
CPU
3. MOTHERBOARD
4.
RAM
5. CATCH ALL PHRASE

ANY DEVICE THAT MAY BE SHORTED CAUSING YOUR
PSU TO TURN OFF!!
did anything change in your computer setup just before the problem?
is there any beep codes given before it shuts off?
there are ways to give the powersupply a test not hooked up to motherboard but not for the faint at heart and\or may kill you!! not reccomended by someone not electronically inclined.