Has this PC been running OK for a while? Or is this a new box?
If its been running for a while, what did you do to it recently?
You can locate where the power switch and the reset switch are plugged into the mobo. Remove both jacks. Then momentarily touch a screwdriver to the two pins on the motherboard that should be connected to the power switch. ("Power" will be marked on the board next to those two pins. The PC should start up and stay up.
If the symptom doesn't change, then you have a psu or mobo issue. The next step would be to swap in a new psu to test that out.