i don't suppose you've tried turning off you computer as uaual, but instead of powering back up, turn off you psu via its tiny switch, then press the power button to drain all residual power from the pc (around 10-15 second push is needed), then switch on the psu and see if the pc powers on afterwards.
pc's refusing to power straight back on could be down to a couple of things, firstly as others have mentioned above a failing psu can be one, but another cause is a failing motherboard, have you had the side panel off and looked closely at your board, you need to look at all the capacitors and check none are bulging or leaking, if you find anything that looks funny post a picture up for us to look at.
but i'd say the issue is either the psu or your motherboard (check your board as thats easy to look at, but don't be tempted to open your psu)
pc's refusing to power straight back on could be down to a couple of things, firstly as others have mentioned above a failing psu can be one, but another cause is a failing motherboard, have you had the side panel off and looked closely at your board, you need to look at all the capacitors and check none are bulging or leaking, if you find anything that looks funny post a picture up for us to look at.
but i'd say the issue is either the psu or your motherboard (check your board as thats easy to look at, but don't be tempted to open your psu)