Do both units seem to function properly during this condition? Is this a simple Sat-audio out --> stereo-audio in connection, through RCA cables? There's no amount of impedance mismatch that would cause this. For one thing, the input impedance isn't affected by the power switch. It almost sounds to me like you have either an extraordinary ground loop, or an actual component failure requireing proffessional service.
If the AC plug of either unit isn't polarized, try reversing it. Also, make sure both units are powered from the same receptacle. One may be reversed. Slide the tips of your fingers gently across bare metal on both units, (like a Quiji board), and see if you feel a subtle vibration. (One unit at a time.) Thats an indication that the chassis is "hot".
Artie