I don't see a Chateau 28A in the 2020 Brochure (there is a 28Z). It says the 31W is the only one with an Inverter so we will assume you don't have one.
If you hear the solenoid clicking when you press the Emergency Start switch, that is a good thing. If the house batteries won't boost the chassis battery to start the engine, that could mean the house batteries are weak and need charged; especially if you are not plugged into shore power. However, of the chassis battery is totally shot, has a shorted cell, etc., that could hamper the house batteries efforts to start help start the engine.
You can use a 30A to 15A adapter to keep the coach plugged into a regular 15A house outlet so the house batteries are maintained. However, you need to have the Use / Store Switch in the "Use" position for them to charge. Make sure you put the switch in "Use" (so the red light is on) and then when you plug in you can be sure the house batteries are charging.
It is possible something is draining the chassis battery up front. It is also possible the battery is bad if they did not check the specific gravity of each cell.
It is also possible there is a loose battery cable. I have seen loose ground cables make it look like the battery is dead when in fact it was not. I would check the battery cables at the terminals (take them off and then retighten them to make sure they are both making good contact and secure) and then follow the cables as far as you can to see if they are tight.
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