Remove the board from the case to eliminate possibility of a short circuit. If you can look down on the motherboard and see any swelling of the capacitors - those small cylindrical parts - that would indicate a problem. You can then remove the heatsink and carefully remove the CPU to examine it for bent pins.
Clean off the lid with an alcohol wipe before putting it back on the board. Put a small blob of thermal paste in the centre and allow the heatsink to spread it out evenly. Make sure it's clipped on firmly then power up the board to make sure the fan is working.
Power off and if it really doesn't have an onboard graphics facility, add a card and connect a monitor then add a RAM stick and turn it on again. If it works, power off and add more RAM. Piece by piece you will have eliminate all the possible faults except the shorting. If it behaves well at that point, does it still do that back in the case?