Just had the same problem with my 2002 525i. Very simple fix it would seem, but it cost about $300 or so with labor. I'm not sure what's involved with changing it yourself so I can't advise you on that. The part number for my car is 64116923204 and has a BMW Catalog price of $88.16 but I think the dealership charged me a hundred and something. If you can change it yourself, should be a relatively inexpensive fix.
You should check out this site for part numbers and diagrams. Just put in the "last 7" of your VIN and you can get all the part information for your car.
RealOEM.COM * Online BMW Parts Catalog
Good luck.
