Try using engine starting fluid. My generator regulator/priming solenoid is bad, so it is hard to start, but runs once it is started. I use engine starting fluid to get it going quite often. I took it to Onan and this was the diagnosis. To take it out and fix it is a P.I.T.A. and expensive. I just take the air filter cover off and spray the air filter, closer to the carb. Starts every time.
I would try everything Kheller says. This was all good advise. I did all this and still had problems, so I took it to the dealer. I promised myself that if I ever took this genny out, a Honda was going in it's place.