No Power unless plugged in to shore power!!! Please Help...

since the batteries test ok it sounds like the converter to battery is ok. The battery should be feeding a fuse box located close to the converter. You mention that there is no 12 volt power... then the co2 and lp detector should be alarming and beeping. Maybe you have a fuse you think is ok but actually may be bad. try taking some of the fuses and move them from one slot to the other. Just have to make sure they are same size rating.