It sounds like you didn't use the right wire for ground. Many cars don't have ground wires in the original connector plugs. They use a separate ground strap or wire. You will often get a ground through the antenna cable's outer shield but that is a very poor ground and often intermittent.
Many people use an ohm meter to find the ground wire in the original connector and just look for one with very low resistance. That ends up being misleading because there will be a tail lamp wire that reads very low resistance through all those bulbs. That circuit in the original radio is to tell the display to dim. There is another very low resistance wire going to the dash lights. That circuit tells the radio how much to dim.
You might check the operation of your tail and running lights. If you used that circuit to ground your new radio, the fuse would have blown because that circuit is now shorted to ground through the antenna cable. The bulbs in all four corners of the car will have low enough resistance to act as a ground for the radio. If the brake light bulbs have less than a perfect ground themselves, a little of the voltage will back-feed onto the tail light circuit when you press the brake pedal. That can also raise the ground voltage for the radio and make it turn off.
Sunday, February 12th, 2012 AT 10:44 PM