I have never seen in my life that a gadget does not work/play properly because its cable is not grounded properly. Grounding is mainly a safety precaution against electrical shocks.
Very sensitive electronics equipment, such as a turntable, may need grounding to the main amplifier. But this grounding is different from what you are referring to.
Your problem may be different. Still you can test if grounding is the problem: To test temporarily, you need metal city water pipes in your home. Then you can use a copper cable long enough to run from the nearest water pipe to the ground pin of the electrical plug of your satellite box. Wrap one end of the copper cable to the ground pin of the plug and attach the other end of the copper cable to the metallic water pipe. Both ends of the copper cable must have the insulator removed or sheared such that bare copper will make contact with the pin and the pipe.