This happened to me when I had a peripheral device (such as wireless adapter, dongle, or ipod) plugged in that didn't have a proper driver or whatever. My Asus usb-n13 dongle would not work and would prevent my computer from starting or shutting down if it was plugged in. If it was not plugged in my computer ran perfectly. That was until I updated my BIOS. Now everything is fine and starting and shutting down like it is supposed to. The Asus dongle works and I'm a happy camper.
So give your BIOS an update if you havent already and unplug everything except the bare minumum (power, monitor, keyboard, mouse, ethernet) to see if it is in fact peripheral devices causing you problems.