inverter makes 120vac from 12v battery power
converter supplies 12v charging power, using 120vac from shore power or generator
i would start by charging the batteries and having them tested
next check output of converter at the converter terminals and again at the battery connections
it sounds like the converter is dead or switch/relay disconnected
generator ran until the batteries lost power.
you might have converter or a charge /inverter combo unit
but in either case its the converter charge section..that does the charging
and you are not charging
