randy,
closr to what I was going to say. I would swap units if you have a similar one handy. all it would take is a bad earth on the amp side of things to pop the RCA shields and introduce noise into the system.
try swapping units.
actaully do this:
radio on, unplug RCA cables. - noise? yes - amp issue ( earth or ground loop) no radio problem be it earth or burnt traces on the board.