I don't know what you mean by converter is charging when the positive wire is disconnected. But anyway...
Check your tank level indicators. One indicator is for the battery. Even if the battery is dead, it will show the output of the power converter while on shore power - should be 4 lights.
Assuming that's ok, check the mini-circuit breakers near the battery. They're covered by red rubber boots. One of them has a teeny-tiny reset button. If that's tripped, the battery will not get anything from the power converter to keep it charged.
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