450, keys no longer work, receiver defective

Hello, the following problem: the smart (bj 2003) no longer reacts to my normal key as well as to my replacement key at all. Also no flashing up. Since the car is switched off in reverse and the immobilizer prevents me from setting it in neutral, I can not pull it to the next workshop. Did the professionals say “let the keys learn again”. Someone came, the keys have learned again and said that probably the radio receiver in the car (the one under the hand brake) is defective. If I would switch it off, the keys would work. Send the keys, he also tested with another device. If I temporarily installed the radio receiver (which definitely works) in the car from another smart, still doesn’t work. Now, at the moment, we have the theory that a working radio receiver in the car has to be so that you can learn the keys. Is that correct? Or would someone have another idea of what it might be like or how to get the car in Neutral? Many thanks for your help and a nice rest week Jürgen