How's the reception on your onboard stero with the engine running? Sounds to me like your alternator is throwing electrical interference down the circuits.
If you hear the motor through your stero that's a pretty good verfiication of that.
Ferrites (small magnets) are one solution - and recommended for delicate electronics. Easy to retrofit as well - just go to radio shack, get a couple and slip them over the DC lines in the back of the power panel. Actual results may vary depending on how big the problem is.
The real solution is to root out the cause (again, likely the alternator) and fix it there with proper grounding and isolation.