Jay, a Alan pointed out in his excellent reply, the fact that the "cheater" plug worked shows that you have a ground loop. This is caused by there being more than one path to ground in your equipment rather than the desirable single point ground and has nothing to do with the "condition" of the power coming from the outlets. There are safer ways than using the cheater to stop the hum, but they don't require replacing a $1 item with a $250 one. Just to touch on perhaps the most likely cause, if you find that disconnecting a cable TV feed also stops the hum, you can use the item Alan mentioned, such as
this one.
