The alarm on my 88 300E goes off anytime I lock the car from either door. The car has a Blaupunkt radio CD player. Can that be the problem? I did a search and found contradictory opinions about a special wire that needs to be grounded is an aftermarket radio is used. If that is true, which wire is that?

Did you try locking the car from the trunk? If the alarm does not go off, you need to clean the door lock or replace the door lock. The door lock has the mechanism that arm and disarm the alarm.