I like the PD4135 I installed in my 1977 Trillium
at 7V your battery is a goner, take it to the auto parts store of your choice and get it tested.
Secondly, do you have a four wire plug or a seven wire plug. Typically a four wire plug will not charge a battery from the TV.
Third, my PD4135 does a fine job charging my trailer battery when I am using shore power. I also have a portable solar panel
. And my tow vehicle charges the battery too. Mine is wired per the wiring diagram over on the document center mentioned below.
On my 1300, there is a fuse in the front gaucho bench. Hard to spot. I switched mine to a manually reset in line breaker, and have another one on the battery (on the tongue). My trailer originally did not have a battery.
Nice wiring diagram over on the document center which helped me a lot.