Assuming this is what you got...
The problem here is the ground loop. The voltage reference for your signal is the "0V" point at the source (in this case the computer playing the music). That is, the computer outputs an audio signal voltage referenced to its own ground.
The stereo is also connected to chassis ground, and it inputs a signal voltage referenced to its own ground.
Since these two grounds are not the same, due to current flowing in the chassis, any voltage between the chassis grounds of the source computer and the stereo is added to the signal.
In addition, the current drawn by both devices is not constant, so even if nothing else in the car was drawing current, their ground potentials would still be different due to their own supply currents flowing in ground.
There are several solutions:
- Isolate the computer from the chassis ground with an isolated supply.
This can work, but the isolated switching supply will add noise of its own, mostly common mode.
You can either use an audio transformer (easy to find, usually sold as "ground loop breaker", pretty cheap) or add a differential receiver. In both cases, the goal is to read the computer's output signal, referenced to its own ground, and output a voltage that is referenced to the stereo's ground, thus removing the noise between both grounds.
The easiest solution would be to use a SPDIF TOSLINK digital audio connection, which is isolated due to being an optical fiber. But you won't find a TOSLINK input port on a car stereo. Another solution would be to transmit the audio using bluetooth.