Grand Theft Auto 4 (GTA 4) Message Board  

Just tried it, got the same results, but fixed it in a really odd and simple way.

Once in a car, select Independence FM. It'll start playing faster than normal. What I did at this point was enter the pause menu, go to Audio, and manually scroll away from Independence FM and then back to it 2 times. On the second time I came back to Independence, it started playing like normal. It was weird, but that's how I got it to work.

You may want to try the same, see how it fares for you. You'll have to do it every time you open up the game, though.