This sounds like you have a cold solder joint inside the radio these can be difficult to find. I would try to get a used unit or replaced it with an aftermarket unit.
Here are diagrams to help you remove the radio for repair or replacement.
Check out the diagrams (Below). Please let us know if you need anything else to get the problem fixed.
Images (Click to enlarge)
Saturday, February 11th, 2012 AT 6:41 PM