SOS! Battery died while hooked to shore power.

Another remote possibility...Battery worn out.....Check water level,and if possible....Volts with a load on it.

At this age,4 plus years,batt could be weak.you just never know how good a battery is so if you do the other things also check the battery.
battery could be about 5 years old in a trailer of your age they dont always put brand new ones in.....the trailer manufacturers buy .... by the pallet load and they could be old