It requires a physical diagnosis to confirm, but that sounds like the transfer case splines (output to front driveshaft). The dealer approach is likely to replace the transfer case. If you don't have a relationship there, try an independent garage that is familiar with BMW.

Look at posts #10 and #15 in this thread, and the subsequent discussion. There is a replacement spline offered by a poster in this thread, and several members have had good results with his work.

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