Actually sounds like a psu issue to me. If the system won't power back on without unplugging it, its a hardware issue not software. Try a different psu.
+1.
Most probably a PSU issue. Also check the computer with any other PSU as fast as you can, since a bad PSU can damage other components on your computer.
Good advice. If it is not the psu, am I right in saying it could be the mobo?