Sounds like your use/store switch is set to store. With the switch in the store position, the converter powered by shore power or the generator powers all DC devices. With the shore power or the generator off and that switch is still in store all DC outlets will not be powered. But some AC outlets will still be powered like the one for the TV if the inverter is wired directly to the batteries and not through the use/store switch.
BTW, you combined DC and AC devices not working in your description above, but my theory deals with that.
David
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