When u swapped out the radio, did u ground the pigtail wire that went to the back of the radio with a clip? It clipped directly to the back of the radio chassis, not to any electrical connector. This is the wire that is designed to activate the factory alarm in case the radio is stolen. Back in the 80's radio theft was a huge problem, and it seems that MB went to all sorts of extravagant measures to protect the radio. Make sure that wire is properly grounded, all the ones I have seen have been black with what looks like a spade connector on the end of it, otherwise it will cause all sorts of intermittent problems with the alarm.
Best wishes and take care,