Normally the engine alternator should start to charge the house batteries once the engine batteries have been topped up so it is possible that the engine battery was down a bit so the split charge system didn't connect (depending on the sophistication of your system)
To get the generator to start, I suggest you start the main engine and run it at fast idle for a few minutes and then hold the emergency start switch on for at least 10 minutes before trying to start the generator.
Trouble is this may not work depending on which battery is used to pull in the emergency connect solenoid. If it is the house battery - which is likely - there may not be enough volts to operate the contactor. In that case you might need to bridge from engine to house batteries using jumper leads.
Or you can plug it in at home - where if the engine alternator hasn't had enough time to get the house battery volts up to around 10, your on-board charger might refuse to switch to charge because it figures there is something wrong.
If that happens then you might have to find a regular simple single rate charger and hook that up for several hours to bring the voltage up high enough for the on-board charger to stop sulking and do its job.
Have fun
Oh yes - if the water level has dropped below the top of the plates exposing them to the air, some damage may have been done - but to get them going again, add distilled water ONLY ENOUGH TO JUST COVER THE PLATES by 1/8". The fully charge the batteries by whatever means works and then top up with water to the BOTTOM of the split ring (which is usually easily visible when you look in - might need a mirror and flashlight. Eye protection is worthwhile just in case)
If the water level is low and the plates are covered, then wait until the batteries are fully charged before topping up.