The engine is connected to the transmission. The transmission is connected to the transfer case. It transfer power to the front and rear axles via two driveshafts.

It is possible that there is something wrong with your transfer case, but we don't have enough information to agree or disagree with your dealer. If you are not confident in the dealer's diagnosis, suggest you get a second opinion from someone who can lay hands and tools on the vehicle. It is too difficult to guess at it over the web.

In answer to your other question, yes, it could be a sensor but it apparently isn't in this case. Your dealer may be able to tell you what codes it is putting up. If the dealer did provide a written estimate, or a list of the codes, and you post that information, we may be able to comment further.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue