X2 on likely a bad fuel pump. Same thing happened to us. Our model 4KYFA26100K Onan has a "prime" function on the start switch at the generator which runs the pump without the noise of cranking the starter. After the generator shuts off by itself, try holding the prime and listen for the buzzing sound from the pump. No sound, bad pump.
Replacing the pump isn't a difficult DIY job, but the control unit had to be removed on our Onan to get access to the pump. Replace the filter while you are at it. Disconnect shore power and battery negative terminals before anything else.