Running the motherboard without a case is a common technique used by technicians to eliminate any weird grounding and shorting issues or mechanical stresses. It also makes it much easier to swap the CPU if that's required. I normally do my bench testing on top of a cardboard box, with a static free bag or foam between the bottom of the motherboard and the cardboard. You don't walk away from a test like this or you might come back to find the box on fire! If your motherboard powers up on the bench with the same power supply that you used in the case, you have a geometry problem. Ideally, you should have a spare power supply for bench testing if you're going to do regular repair and testing work.
Make sure some standoffs aren't higher than others, putting unacceptable stress on the motherboard. Check that every standoff appears under a screw hole. The easiest way to be sure is to count the standoffs, count the screws, and make sure there are no screws leftover after you install the motherboard.
There could be a short caused by a misplaced standoff, a loose screw, metal chips from shoddy materials. I've encountered standoff shorts that produce an endless string of beeps like RAM failure, without damaging the motherboard. There's also the possibility that the case geometry is so messed up (out of square or level when the cover is forced on) that it's putting an unacceptable mechanical stress on the motherboard resulting in an open circuit. If you can't find the cause of the problem, don't hesitate to try another case and power supply.
