To eliminate the hdd as the problem, unplug the ps3 from the wall. remove the hdd and then plug back in. turn on the ps3 WITHOUT the hdd in it. Don't worry it doesn't harm it at all. If the problem is the hdd , you will see a "data storage not found" message on the screen and the ps3 will not shut off.
If after you remove the hdd, and the unit still shuts down and you never see that message ...the problem is NOT the hdd.
90% of the time when this happens, its actually the motherboard not the power supply. The power supply is quite large and incased in a tough piece of plastic. The motherboard on the other hand has 2 very thin metal plates on each side, with the weight of the power unit, cd/bluray/dvd unit, the fan...all resting on it, if it fell it probably jolted something.