The problem is not so much a "dirty" ground but a different ground from your AC line.
The grounding rod for your AC line is in a different place then the grounding rod for your satellite system. When you hook either the TV or Sat box up to your system this will create a ground loop.
The cheap isolation transformers will not work correctly as they totally isolate both the signal and the ground. With cable modems and interactive satellite, you would still need to pass a DC signal through the transformer from the control box.
A bit more expensive version will isolate the grounds and still allow the center conductor to pass DC.
MCM Electronics sells one for $20.00
[Ground Isolation Transformer
A more expensive isolator using a capacitive based design is sold by Jensen Transformers for about $60.00.
Cable Isolator