If it starts and runs and stays running, but there's no power to the coach, the problem most likely is not the generator itself. It has control circuitry to shut it down if it is not producing power (for safety, as one main reason for no output is an internal short in the windings that can get hot and cause a fire).
Assuming the shore power supply works reliably, the problem would be in the wiring between the generator and the RV's electric panel. I would have the transfer switch checked out, assuming you have a transfer switch--which you do if you don't have a socket to plug the shore power cord into for generator use. This should be a relatively straightforward repair in any case.
One easy thing to check is the output breaker on the generator itself: flip it off and then back on. Sometimes when they trip they don't look tripped.
Good luck whatever you end up doing.
3200 hours is a good bit more than most RV generators get used, but the Onan generators have a long life when used consistently and maintained properly.