2001 Ford Taurus Radio Problem

I have a 2001 Ford Taurus that hs a radio just giving me fits. It all staarted a few months back when the radio would intermitently cut out. Then I would notice at times the clock would dissappear. It kept doing this and getting worse until at this point now the radio no longer works, the CD player doesn't work and the clock only works until you turn the ignition to on or accessory at which point it goes out. I tried getting a new radio from a salvage yard, plugged it in and got the same results. Could this be an issue with a ground wire? Any help would be greatly appreciated since I am not really good with electrical issues. Thanks in advance.