there are two wire in the kenwood wiring harness a yellow one and a red one, one is for permanent power and the other is for when the car is started or is on accessories. It is often the mistake of many people to join these wires together then to power which results in what you are experiencing. connect the yellow to the battery and the red to a power source that comes on when you turn the car on and try tuning in the stations if this does not work then change them around. it should work then. with the stereo cutting out it could be a number of problems such as a speaker earthing out or overheating also depending on the type of car it went into because of wiring set up of the car or as simple as the stereo being an old one you have not given enough info on your set up
picklo
April 2010