Power Supply Problem

I think I may have a power supply problem with my aunts computer.  I built it about 2 months aga and it started having problems off and on since then. What it will do is either not power on, or it will shut off unexpectedly. Its a toss up one which one it does more.  I have since replace the power supply, it tested dead, and now it is doing the same thing again. The first one was a generic 350 watt supply. The second is a 400 watt powmax that I had sitting here. Here is the system:

Athlon 64 2800+
512 Ram
2 hard drives
2 cd drives
biostar nForce3 250gb motherboard

Anyone have any ideas on why its doing this or what I can do other than put aonther supply in that may just end up fried?