My Panasonic head unit had a trouble on the RCA outs , an open ground I believe on one. Trouble was on a brand new out of the box unit. This caused the same trouble you have. New unit no problem.

Don't get me started on my piece of junk 300 dollar Pioneer I bought @ Futureshop. It's had crappy radio reception, cutting out, and static since I bought it.. and Futureshop only bench tested it in the car.. It's called you need to drive it to actually hear the problem.. cars move when playing the radio.. LOL.