If you google "The Dead PC" you find the most common troubleshooting is to make it smaller.

I can usually get the parts down all the way to just the motherboard and PSU on cardboard (no case) and if those don't power up I'm looking at the possible bad part or parts.

I don't find it's always the PSU when it powers up for a second or so. It's usually BAD CAPS (see google) or some other cause.