I suspect that either the RV's converter/charger is failed, or a circuit breaker between the batteries and the converter is popped. Since you get 4 of 4 LED's with the alternator supplying the charge, it seems the converter is the problem. With the generator running or when you plugged into shore power, you should see 4 of 4 LED's showing that the converter is charging the batteries.
Be aware that it takes many hours of charging to get the batteries back to life after being run down that far. So you would need to get the converter (or an external battery charger) going for a good overnight if the batteries are ever going to charge.
If after a healthy charging time the batteries still fall off quickly, then they are truly dead.
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