[andrewas]

I have seen motherboards that get part-fried or just plain old and behave very much like you described. But its not common and Ive never seen it in a machine this new.

I suspect either a dying PSU or maybe just a dodgy switch. You could try getting another machine and trying its switch and PSU with yours. Goes without saying that you should also check all the cables and connectors in case one of them is lose or damaged.