It sounds like the stereo jack is not connecting, if the headphones work with no issues then it sounds like a problem with the stereo jack. Can you switch the jack from the stereo? If the female part of the TRS connector (part in your phone) is recessed depending on how the male connector (from the stereo) is made it may not be able to penetrate deep enough. This would cause it not to create a circuit and the phone would not realize it is plugged in. You can get an extender from a electronics store which may work better, you may even be able to try it out at the store.
Amazon.com: 3.5MM Extension Cable: Electronics
Just an idea of what you would be looking for, likely you would not need something this long.