Radio doesn't come on until the car is turned off?

It is a problem with the retained accessory power system that is controlled by the body control module. There is not a lot of information on diagnosis of this system, and it could come down to power moding of the ignition switch, or a fault with the body control module. Ideally, it would be helpful to be able to see what the data is reading through the use of a scan tool. The radio recieves hot at all times power, and is controlled through data bus from the body control module. If the body control module is recieving incorrect input on ignition position, then it could be doing all it knows to do. If it is recieving correct input, then it is possibly performing incorrectly. This is all you get for a description of the RAP feature.

Retained Accessory Power (RAP)
The retained accessory power (RAP) feature allows the use of the entertainment/phone system after the ignition is turned OFF. The BCM controls this feature via the Class 2 serial data circuit.

The RAP feature is enabled when the ignition is in the ON position. RAP will not enable, however, when the door open and the ignition is turned to the LOCK position.

The RAP feature terminates when one of the following occurs:

†After 10 minutes with the ignition switch in the LOCK position.

†With the ignition switch in the LOCK position and a door is opened

†When the ignition switch transitions to the START position

This happens when the BCM goes out. Here is the location so you can swap it out, you can get a preprogrammed unit by searching Google or Ebay. Check out the images (below). Please let us know if you need anything else to get the problem fixed.