Sounds like the Wheel Sensor issue to me.

You need to go into the 'hidden' service menu - go into Setup, then press and hold Menu for about 10 seconds and the menu will change.

Go into Sensor Check and there will be an item called Wheel Sensor(s) - when you drive, you should see this figure increase/decrease with speed. If it reads zero, then it means that you (probably) have one of the fits with the incorrectly wired loom. Its a fairly easy job to fix.

I had exactly the same on my E46 and after much searching and questions on the net and 5 visits to the dealer, it was sorted.

If it isn't the wheel sensor, then I don't know what the issue is as that seems to be the one thing that will provide the symptoms you describe.

Check it and let us know.....