First thing to note - this is nothing to do with the remote key battery
. You can start your engine with no battery in the ignition key. The batteries are only required for the central locking system operation.
The power for the key electronics for Drive Authorization is supplied from the EIS electronic ignition switch control module (N72) via induction coil and IR circuits. So there has to be something inhibiting the Drive Authorization system, which permits the key to turn forwards from posn 0 to posn 3.
As your spare key works fine, the problem is not in the car..
If the end of the key that contacts the EIS is not dirty, preventing IR transmission, it must be that the infrared transmitter/receiver circuit inside the key is faulty.
The circuits can be revealed by sliding the key cover off, and (using magnification) you might see a bad connection there on the printed circuit. You must use a miniature soldering iron to do any repairs, or you can do damage with excessive heat with a 'standard' iron.
MB dealership can supply a new 'spare' key, but you will be expected to provide some evidence of vehicle ownership and ID to prevent fraud. It's not cheap either....