I have an Onan 5500 that has always started easily and run fine. Has about 240 hrs. I have a guy doing some inside work today so I showed him how to start it and turn the heat on as it was cold. He ...
The fact that OP's generator runs under load but shuts down when unloaded is a classic case of governor issues. There is an adjustment procedure for the governor - If it does not automatically regulate under different loads than start looking at replacement or sending to service.