That dealer sounds like nothing more than a parts swapper. As I understand it, the DAS Xentry diagnostic systems don't tell them "change this part and if that doesn't work, change some other part". That systems scan, coupled with the WIS, should narrow the problem down right away.
For those interested in the technicalities here, I've dug out some WIS details on the DAS for this car. If you don't reach the DAS requirements with the key in posn 0, you cannot turn the key to posns 1 & 2.
Now the OP says that the key will not turn (at all?), so we have to assume that it sticks in posn 0. This is where the steering lock is released, and you can hear the lock mechanism move. This is important to know, but has not been stated. I'm not sure what key position turns on the radio.
Also shown below (for interest) are the diagnostic tests available in 1990 to test the operation of the DAS using the old HHT hand-held tester plugged into the diagnostic socket. It is clear that the key, the EIS and the steering lock can all be validated by the MB test equipment.
My money would be either on the IR transponder in the remote key, or the IR transponder (L11) in the ignition switch, which is replacable. I doubt if the EIS is the problem.
A new (spare) key is required anyway, so should be ordered now.
With the test gear available at MB, there is no reason for any doubt about the operation of these components without part swapping!