Sounds to me like a jumper. Did you wire your power switch yourself? I have had that happen before, where the power switch was a little messed up and it would shut itself down. As far is it actually running and then shutting down tho, that probably isnt the problem.. Its definatly not your hd, i mean, it could be your hd because of a bad sector, or just straight ****ty media, but its definatly a compatable HD.
Try swapping out your ram with another stick, alot of times corrupt or unallocated memry acts like that. Is your ram have a cas rating of 2.0 or 2.5? and is it allocated or unallocated, was it error checked at the factory....these are just a few of the things you should make sure of before you buy ram.