This is a little off your original question, but make sure that you carefully check out all the battery wires and grounds before investing in a new starter.
I replaced a starter, which is a pain, and later found that it was poor connections in the wiring. Do a search, there are good suggestions to R & R the starter. Of course, when the cheap rebuilt starter I used, failed. I had a perfectly good one in the trunk to replace it.
Here is a thread link to check out http://www.bmw2002faq.com/component/option,com_forum/Itemid,57/page,viewtopic/t,282924/highlight,starter/ There is another useful link within that thread.
Good luck