Alarm goes off while driving
 

I own a 1988 420sel and the alarm continues to go off even after I put the key in the door. I was wondering has this happen to anyone if so can you help me out.

it is common for that vintage alarms to do that, in the meantime i suggest you disconnect it, the alarm module is located under the passenger side floormat area, the module will say becker on it, unplug both connectors, the likely problem is in the door tumbler micro switch, you can either order a new handle assy, i believe they are over $300.00, or install the handle assy from the passenger side

Hello Chief!

I had the exact same year and model, and the same exact thing would happen to me.
Once you have unlocked your door, do not remove the key - open the door, and unlock the door again. This should stop the pesky thing from going off, after you drive away.