The fact that the lights got brighter when you started the engine is an indication that the batteries are indeed very low, if not completely dead. The engine alternator was simply providing the DC voltage while the engine was running. Regardless of the brand of motorhome, the brand and type of converter/charger installed and whether or not any disconnect devices are employed, it’s obvious the batteries are not receiving a charge while the coach is plugged in to shore power.
If you can measure an increase in DC voltage at the battery bank when the coach is plugged in, then the battery charge circuit is at least complete and probably working. If the voltage does not go up when plugged in, look for a blown fuse in the charge circuit in the converter/charger. Look also for any electronic disconnect switches that totally isolate the battery system. It’s common on some coaches to employ these during storage or a lengthy downtime. If they are activated while using the coach, it literally takes the batteries out of the system, meaning you cannot charge or discharge them.