In your car, the whole frame is attached to the neg. terminal on your battery, so it is all ground. The reason there is a ground is so that the power going through the electronics in your car has somewhere to go after it has supplied enough current to your circuit.
It can cause the speakers to hum if your stereo is grounded to one source (the car)and your computer is grounded to another (the case). This is because they are two different grounds with different properties, in order to fix the problem you could ground your computer to the car. All you have to do is attach a wire from the case (or the MB ground screw if you don't have a case) to the frame of the car. Note: paint is a resistor, so you will have to attach it to bare metal.
I had this exact same problem with my in-car MP3 player; I was using a DC-AC inverter and picking up a lot of 60Hz hum from it. I tried all sorts of filters and then I simply ran a wire from the PC's case to the frame via an already-in-place bolt for the trunk latch. Viola! The noise stopped.
Attaching a ground where there is paint is a bad idea -- try to sand the metal in the area of contact to make the ground better. Actually the threads of the screw make a good ground themselves even in places where paint is present, but it's not a bad idea to clean up the surface as well.
Actually other problems relating to grounding include ground loops. It is often a better idea to run a ground lead directly to the negative terminal of the car battery or to the engine block (often a great common point for grounding!) than to simply attach to whatever part of the body is close to the device you're trying to ground. High-frequency noise ranging from static fuzz to full on wailing can get introduced into the audio signal if the grounds aren't "common enough", i.e., the vehicle's body isn't a perfect conductor throughout, so it's best to try and ground thing such as audio equipment as close to the same point as possible.