[beagleboard] Processor gets very hot when dc-supply is pluged in

You damaged it somehow if it gets as hot as you say. It should run around 50 degrees C at 1GHZ. Best I can suggest just is to request an RMA and let them look at it. Not being there and seeing what you are doing and what you may have done, it is rather difficult to suggest anything that may repair the processor if it is indeed damaged.