I would not hook that new battery nor any battery up until I knew that I have 12vdc coming from that converter and that the + lead for the battery and the - lead are labeled and have the proper polarity . Doing this keeps you from hooking a battery up backwards... An absolute no no.
That said, you have no power coming from your converter, other wise your jacks etc would work.... The converter should provide power for that without the battery unless the converters protection fuses blew. They both will blow, not just one.
You need a meter to measure 12 vdc... If you do not have one get one and use Youtube to learn how to use it.. EASY for basic stuff. Maybe you have a friend that has a meter and knows how to use it....
If you inadvertently hooked the battery up backwards 2 things are going to happen.....
1.The protection fuses on the PD9200 are going to blow.... There are 2 and they are 30 amps each....
2. You may have fried everything that was on that runs on 12vdc.... LP sensors, Radio, Fridge Jack controller... Hopefully this did not occur...
So a meter first, hook up your shore power, check the Converter output 12vdc/fuses, then the polarity of the battery hookup wires 12vdc and then if everything looks correct.. Remove shore power, connect the new battery up and see if your jacks and other 12vdc stuff works.
Plug in shore power if everything works...
Keep us informed.
Jim