Maybe wire of your satellite cable is not properly connected to the pin or both wire of satellite are short or may be your satellite cable is near to your electric power supply cable if still there is a problem then check what other cable you have connected to your TV one by one.
This sounds like a minor problem, unless the humming is extraordinarily loud. Does the sound start and stop? Or is it continuous? If it's the latter, some of the boards inside the set could be burning out.