Onan Generator No Start

This is just a guess, but I have had the same symptoms with an old 8N tractor. The problem may be a loose connection in the 12 volt system providing power to the starting circuit (positive or ground). I'd disconnect, inspect, and clean the large 12 cable connections, especially those at the battery. I think what is happening is that, while usually a connection is being made, sometimes the connection surface area is small, and when the starter solenoid engages, the weak connection is oxidized by the heat of the larger current flow trying to turn the starter. Thus too much voltage is dropped at the bad connection to enable the starter to crank the engine.