I'd go down to a minimal build; 1 stick of RAM, HDD, PSU, and GPU (unless you have onboard graphics that works, then leave off the GPU) and see if it works, if it does then add pieces one by one til it stops working. If the minimal build doesn't work, I agree with screensavers, sounds like a MoBo issue.
Also, this may sound dumb as hell, but make sure the power button isn't getting stuck. I troubleshot a computer for about 2 hours with a similar problem before I realized the power button (not the acutal plastic button, that popped back out correctly, but the piece inside it that actually makes the connection) was staying depressed and causing it to hard-shutdown moments after powering up.