You may just be hearing the noisefloor of your soundcard. Try an experiment: try playing silence in one of the zones (i.e. find an audio track that has a prolonged silence or a silent test clip, etc.). If you hear the same soft white noise out of the channels you're playing to, then what you're hearing is the noise floor of your sound card. Some soundcards "latch off" when nothing is playing so you don't hear the noisefloor at idle; playing silence rules that out.
If you play silence and get actual silence on one zone, try playing silence in a different zone just to confirm you're not seeing differences in speaker sensitivity. If you get actual silence in the zone where you're playing silence, and white noise everywhere else, then there probably is some kind of software issue. Otherwise, it's almost certainly a hardware noisefloor problem.
I struggled with similar issues myself for quite a while before figuring out a good solution. The good news (if that is the issue) is that there are relatively cheap solutions, but I can't say much more without knowing what kind of sound interface you have and how it's connected to the amps.