First: To fully disconnect house battery you need to life a lead, Suggest negative, ON some Motor homes you also need to lift the CHASSIS negative lead.
Set meter on VOLTS, DC, 20 volt range
NOTE that this is only one of several tests.. You should see 13.6.
ALso measure battery voltage (it should be 12.6 after sitting for an hour or two) if it's like 12.1 hook meter to Converter and re-attach battery lead.. You may see voltage increase or drop.. A DC-AMMETER (you may wish a clamp on model ) should show current near the limit of the converter. (IncreaSe or drop depends on so many variables I can not began to list them all) Also measure voltage again at the battery.
In time the converter shoudl return to 13.6 With batteries connected they should be same voltage.
Most common Converter failures.
NOTE: This first one applies mostly to me: Unplugged (don't work unplugged)
Bad connection somewhere along the current path
Blown Reverse Polarity or other fuse or breaker.
Finally we get to Converter failure. (all other issues).
NOTE: To replace fuses.. UNPLUG from shore power.. Disconnect from Batteries, REPLACE all RP fuses (These are usually 30 amp but you may have 1-2 or 3) THEN plug in, and re-connect.