Here is a typical 30A POWER Configuration Block Diagram...
Might help figuring out what has failed...
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Your 120VAC shore power connection should be powering up the 120VAC Power Distribution when hooked up. This is how your microwave is working now...
Your 12VDC Power distribution Panel is powered up by the CONVERTER/Charger unit when on Shore Power and/or the 12V Battery.
Obviously something is this regard is not working. Both the converter/charger unit and the 12VDC Battery provides 12VDC to the 12VDC Power Distribution Panel.
If the converter/charger 120VAC Breaker is ON it should be putting out 13.6VDC feeding the 12VDC Distribution Panel. This 13.6VDC should operate your lights
Need to check connectivity from the 12V battery to the 12VDC Distribution Panel... Perhaps you have connected the battery terminal cables in REVERSE ORDER... Find the word 'NEG' or the Symbol '-' on the battery case and make sure this is the cable that goes directly to frame ground.
If you did see some sparks when you hooked up the battery terminal you may have now blown the two REVERSE POLARITY fuses as well as a in-line fuse very close to the battery terminals... You need to make sure the cables are put on correctly before replacing these fuses if they are blown otherwise it will just blown them again.
If you study this for a bit it should all start making sense of what is failing...
Roy Ken