How to get rid of groud loop noise from dish ?

If your sat receiver has an optical audio output, use it instead of the coax or line level analog outputs. Cheater plugs may or may not be feasible depending on the complexity of the system and the effect upon the sound quality from other, better signal sources. There are in-line isolation transformers for the line level analog signals, but they are probably about as expensive as a new sat receiver with optical output. Good luck.

Line level isolation transformers can be found economically at most car audio shops; they have RCA in's & out's. These will isolate the audio shield connections from the hyper-ground noise which you're experiencing.
Sometimes though, all you have to do to fix this is to ground the coax's shield to your household ground. Use a length of stranded #20 awg wire, strip off some insulation & attach one end to a household outlet's cover-mounting screw, then strip & wrap the other end around the coax connector's shield, securing it with a small cable tie. This brings the coax';s ground potential equal to your household ground, which completely solved the problem for me. I still use the audio coupling transformers as extra insurance, though it may not actually be necessary.

Just wondering if it is a bad idea to common up the grounds. Would this not put a bit of noise onto your audio component's ground? If so, this would not be good for your noise floor.

There is also a small coax device designed to get the hum out. Mondail makes one, it's called the Magic Box. I believe Audio Advisor and Audio Outlet both sell it.

Simple: attach one end of a wire (maybe with an alligator clip) to the outside sleeve of the satellite TV coax cable (where it enters the receiver) and ground the other end. You can also buy a Radio Shack ground block for cable TV that has a little screw for connecting such a wire. don't spend more than $5 on this problem.