Can you disarm the alarm by unlocking the passenger door or trunk? If so then you probably have a bad alarm switch in the door handle mechanism. As I understand you can't replace just the switch - you have to replace the lock or handle mechanism (not sure which). Try this - unlock the car, pull the door open, quickly twist the key to lock. That's how I dealt with my 91 300SE until I realized that no one was going to steal it and disconnected the alarm. To do so, pull either of the 14(?) pin connectors into the long slim box behind the plastic panel in the passenger footwell. IIRC, the box is marked Becker Autosound or something like that.

Sixto
95 S420
87 300SDL