Just received the key from Mercedes, and tried it.
Unfortunately none of the locks opened with the factory key.
I then thought, that these locks haven't seen a key for decades, so I tried lubricating the locks with plenty of WD40 and moving the key for all possible directions back and forth for a long time, and finally my new key starts working on the passanger's side door lock!!!

So I'm happy now, that I have a backup solution if my remote fob weren't open the car, I can get inside by opening the central at the passanger's door.
Thanks a lot for the tip, it finally really worked, and the cheapest solution!!!
(The key was about 20 USD and was arrived within 2 weeks.)
Problem solved, case closed!