I'm having exactly the same issue with my 5 month old PC and I'm hoping it's the PSU as well. Switch off PC, power back on, motherboard LED comes on showing power comes through, when I hit the power on switch there's a momentary flash from the LED on one of the fans and then no power, doesn't happen again till I let the power dissapate from the PSU.
Will be testing tonight by firstly, removing everything out the case, re-seating CPU (with some new goop, may as well). Then trying with existing PSU out the case, failing that I'll try my old PC's PSU (Ironically it's more wattage than my new one).