The generator starts using the house batteries. Are they fully charged? If you have a multimeter check the voltage at the power terminals located at the lower rear of the genset. As others have mentioned a loose connection could cause your symptoms. I would make sure to trace and check the ground wire where it connects to the Freightliner chassis.
Also, are you holding down the start switch long enough? When you first depress the button to start the unit the Onan fuel pump "clicks" bringing diesel from the main chassis fuel tank to the unit. And the unit won't crank over until the glow plugs have sufficiently warmed. That can take up to 30 seconds if the ambient temperature is low.
2014 Seneca 37TS
Toads: 2019 Ford Edge ST or 2013 Ford Focus ST