Just by plugging into Shore power should not deactivate one of these alarms.
I would suspect the output of your Converter. Considering your symptoms of the unit operating properly on the battery and not when plugged into Shore power, your Converter may be putting out the wrong voltage. Get out your manual on that new Converter and see what they say their 12-VDC level should be both with a load and with No Load.
Just in case your Converter is putting out a very low voltage because of the load from uncharged battery's let it run for an hour or so and see if the light comes ON.