It could be a bad converter, however that seems to be working while you are on shore power. That does not rule it out, but it is the most expensive to replace, so I always check the cheap things first. One question I didn't ask - do you have 120v power on generator? Do your microwave and your A/C work? If they do, then the breaker from you generator is not tripped. Next culprit could be the transfer switch which automatically switches between shore power and generator. Many people have had problems with the connections in the transfer switch. Could be the connection to the generator is bad. If not, then it could be the converter/charger.
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