If the generator has been sitting for awhile and not started at least once a month, then likely the carburetor is plugged up and will need to be replaced. They are so small (compared to a car) that even a little bit of varnish will totally plug the jet. When sitting for any length of time (like winter) they need stabil or a similar product in gas and should be started monthly.
There have been some problems lately with Onan 4000s with the fuel pump. But usually the symptom has been fuel leaks. Onan has been replacing them under warranty. Get the serial number off the unit and check with them.