The generator supplies AC which powers the converter which charges your coach battery. If you have the ability to read voltage - measure the battery voltage when either the generator is running or connected to shore power - should read about 13.6 volts ... if you don't have the equipment look at the interior lights, they should brighten when hooked to shore power.
If you suspect a bad converter - look for an auto reset circuit breaker (Google it as it looks strange) near the battery - if that goes south then your converter can't charge the battery. It's also possible that the fuses on the converter itself have blown.
