The generator or shore power, supplies 120 volt power to the converters, so at least something is working.
Most generators don't have seperate charging systems but depend on the house charging system to keep thing charged.
If the shorepower isn't powering the converters, you may have a wiring, transfer switch or adaptor problem. Is anything else NOT working on shore power ?
With the main engine alternator, that's a different system. Look for an isolation relay. They are, most times, the same relay that the boost switch uses, so hit that switch, on and off, to find it. They often fail.
Once found, let us know. There is a simple test.