Breadboard it outside the case. Set it on an insulated surface and connect JUST the Power Supply, keyboard, memory, and monitor to the integrated video. Don't connect any gfx card or drives. Momentarily short the 2 pins that the power switch would connect to to start. (If you feel uncomfortable doing that, maybe you can drag the case close enough to plug in the 2 start button wires and use that.)
Be sure the 24 pin cable is securely in the header and that the clip on it is over the header's little nub.
It should start and produce a display. If not, and you are sure the PSU is OK, I would sent it back.