get one these digital voltmers from LOWES-WALMART-Any number of auto parts store - even harbor freight or northern tools... They cost $10-$20 and some store was giving them away at one time.
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Every RV'er should have one of these in their RV TOOL box...
Like stated above measure across the battery terminals and if the battery is fully charged it will read 12.6-7VDC... A totally failed battery will read less than 10.5VDC. If you connect your converter/charger to shore power then the DC voltage on the RV Battery should jump up to 13.6VDC telling you the charger is working...
If you don't see the 13.6VDC then you need to start looking for DC voltage coming off the converter terminals. Perhaps a cell has gone bad in the battery and has blown an in-line fuse close to the battery terminals. Another possible problem is the battery terminals on the battery have been installed in REVERSE POLARITY order which also will blow the in-line fuse as well as two large fuses on the DC Power Distribution panel Labeled REVERSE POLARITY. Sometimes these fuses are located on the converter/charger unit.
If the converter assy is not putting out 13.6VDC at its DC OUT terminals and the shoe power is connected then it is possible the converter/charge assy is bad...
Just my thoughts
Roy Ken