Most definitely check out the converter/charger unit. Both the converter and the battery feed your 12VDC Distribution panel and if the converter/charger also bit the dust then your battery will not be charging when you are on shore power. Letting your batteries get down below their 50% charge state will be very hard on them as well and may also be harmed later on.
A fully charged battery shows 12.6-7VDC across the battery terminals. When you plug into shore power the DC VOLTAGE across the battery terminals should jump to 13.6VDC indicating the converter/charger unit is functioning ok.
Most folks that report their Microwave getting zapped due to bad AC VOLTAGE usually find their converter/charger unit also bad. i.e. anything that is normally always ON on the 120VAC side will get zapped.
Since your trailer is 50AMPs then you have two 120VAC POWER ZONES so this may have protected some of your 120VAC items from failure as it appears one of your 120VAC legs went very high AC Voltage and perhaps the other 120VAC ZONE went very low voltage. Only the 120VAC items on the very high 120VAC side of your two 120VAC ZONES that was 'ON' at that may have got zapped.
lessons to be learned here... 50AMP Systems has lots of power capacity to be respected.
We always flip the Pedestal breakers to OFF before connecting up our shore power cables just for the reason... I use to test the pedestals for proper AC VOLTAGE LEVELS but have got alot laxed in doing this every time. These two pictorials show what is suppose to read at the pedestal 50A an 30A connection using a multimeter.
You can also use one of these AC LINE CIRCUIT TESTERs at the pedestal as well using a RV 50A or 30A adapters. If the two lights showing CORRECT do not come on as shown here DO NOT PLUG INTO IT with your shore power cable...
I have one of these circuit testers and a RV120VAC VOLTMETER plugged into an easily viewed 120VAC receptacle in my trailer all the time. This is especially useful to glance at the VOLTMETER before turning on the Air Conditioner. If the AC VOLTAGE does not fall between the GREEN SAFE ZONE I will not turn it on.
Roy Ken