The passenger window motor in my 124 recently stopped in a similar manner.
When I applied power it would click just a little, but the motor would not turn.

A new motor fixed it right up!

Tip:
There is a round plastic bumper mounted under one of the motor bolts that will fall out when you remove the motor. I spent a lot of time trying to figure out what it was and were it went.

It is a stop-limit for the regulator. If you look at the ends of the big regulator gear there is a curved "hook" on each end of the arch.
It limits against this when fully open as well as from the other side when fully closed.

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02 S500
92 500SL
92 400E (Sold)
87 300E (Sold)
83 300D Turbo (Sold)
75 300D (Sold)
74 240D (Sold after 20 years)