Your batteries probably have low water level now. Add only distilled water to them.
You pretty much confirmed that the converter is not putting out power by the battery being dead. Check with a lamp or plug in something where the converter plugs in. Likely that a tripped GFI has stopped power to the converter.
IF the converter has power in, but no power out, then start looking at the fuses on the side of the converter. If they are good, then look for a brand new converter.
BestConverter.com Call and tell them what you have, they can recommend a better replacement. Also let them know if you have a 40 or 50 amp fuse on the line between the converter and batteries, or distribution panel. It would make no sense to buy a 60 amp converter and have it keep tripping the fuse.
You also want to avoid a common problem. If you have a 30 amp converter, then it takes 'forever' to recharge on the generator. In that case, upgrading to a 45 - 55 amp converter and changing out the wire to install #6 wire would shorten your generator run times. If you could relocate the converter to near the battery, without being in the same compartment (Battery gas is really bad for electronics) then a short run of #6 or #4 wire will allow upgrading fairly in-expensively.
You might also consider upgrading to solar power. A 140 watt 12 volt solar panel is only $229 at this place. 140 watts is only about 40 AH daily, about what your refrigerator, propane and CO detectors use in one day. I have a total of 400 watts on my RV, and can watch hours of TV through the satellite system.
SunElec.comEven one of the 140 watt panels will allow you to camp for a really long weekend without needing to recharge. It will put back just a little less than you use daily, but will stay ahead of the loads in most cases.
I have a 'e-meter' that carefully measures the amps going in and out of the battery pack. If I was more than 120 AH discharged, I would run the generator early in the morning to get it back to about -100 AH, then it will make up that much power before sunset. When the battery is most discharged, it will accept the most power. Once over 3/4 full, the amperage even from my 70 amp inverter/charger would be less than 20 amps. Not really worth running a 4,000 watt noisy generator to get back 20 amps at 12 volts (about 240 watts). But in the mornings, before solar takes over, it could put out 55 amps into the 4 golf cart batteries.
Good luck!
Fred.