it sounds like the PSU might be faulty - or something plugged into the motherbaord is holding the voltages down.
first thing to try would be to unplug everything you dont need.
i.e. CD drives, Hard drives, remove all but one memory simm (unless you need a pair to start - then leave in 2) any other cards (except the video card) attached to the motherboard.
Start up and see if you get to the BIOS (or to the point where it says that there are no system disks present)
If you cant get your PC to stay up for any lenght of time with minimal spec
try swapping out the power supply
Again - leave a minimal spec, and add the cards and drives back in one at a time.
restarting each time.
if the PC fails to stay up when you add an item - it is almost definately going to be that part that has failed, or has a faulty cable or connector.
Please remember to use ESD protection when touching anything inside your PC