@totalknowledge: Not really. It can be also a short somewhere. Not in my case of course. Have tested the rig outside the case on a wood table.
I (in my myopic 20 years dealing with my, my work , and my family and friends computers) have never seen that specific behavior caused by a non-psu related short. It has always been caused by a faulty psu. Not to say its not possible, but I don't think that that would be a common cause or the computer not starting, and then starting after unplugging the power supply, then plugging it back in.
edit: made my post a little clearer.