Yes, the GFCI has to have power before rest!
Some things to check are that the outlet where plugged has power? Is there a breaker there that needs turned on?
when you say no lights, do you mean no inside lights or no lights on the microwave?
The microwave light only uses 110 power but the inside ceiling lights are 12volt and work off the battery!
For now, turn the inverter off ot make sure it is not running the batteries down!
If the batteries are down, can you start the Generator? If it starts, then you can try plugging the cord into the generator outlet box.
If you can't do the generator, try starting the RV engine. That is a different battery and should start okay. When it is running, the two batteries will be connected together and that will let the inside lights and RV things start to work when they get power from the engine alternator.
If you find things work when the engine is running, it may be that the coach batteries are run down. One way this can happen is if the inverter is left on and no 110AC power is going to the m to keep them charge while the inverter is using lots of their power.
When plugged to power, it is best to turn the inverter off.
Do you have a way to test voltage?
V