The Coninental my Dad used to drive wouldn't pull in any radio station with the rear defrost on. Really sucks to buy a Premium Stereo and not get to listen to it, doesn't it?
Now, there is actually a TSB for that on the Lincoln Towncar, Continental, Mercury Grand Marquis, and Ford Crown Victoria. However, all those cars have antennas in the glass. The remedy was to move the rear window defroster ground or something like that.
However, I doubt simply moving the ground will fix your problem. When this happened on my Contour, it turned out to be a serious wiring problem with the rear defroster. Basically some of the insulation of the defroster wire in the rear of the car had worn away, and so had some of the insulation on the antenna lead in the trunk. When I turned on the defroster and current started to move, it electrified my passenger's side rear fender and zapped my antenna, making it unoperable. I had to have some wiring replaced, needless to say.
My suggestion would be to take your trunk liner apart and look for any wires with abrasion on the insulation.
This only applies if you radio doesn't work. If your CD does the same thing, then you have a problem with your HU or your wiring. In which case, I'd check the wiring first and then have the headunit bench tested.