Is your Onan EFI or a caburator version? I have an '02 Georgetown with a 5.5 HJAB and I'm having a very similar problem. I found the service manual on line and I'm still trying things.
Mine has the look of a deliberate shut-down by the electronic controller. I'm getting fault code 32 (blink-blink-blink-pause-blink-blink), which the book says is a "failure to achieve sufficient cranking speed". Since it fires up and runs a couple of seconds, then shuts down, with smoke out of the exhaust pipe, I'm very sceptical that cranking speed is the issue.
On the carb models, there's a solenoid device in the base of the carb that closes off the main jet. This is supposed to stop the "dieseling" that used to plague some cars in the early emission equipment days. I though that might be the problem, but even with 12V hard wired to it (not through the "brain") it still has the problem.
One problem I did find was that the Onan fuel pump (mounted beneath the base plate on the forward edge) was intermittent. We got a new one and installed it, but the problem remains. I'm waiting for drier weather before I go outside for more investigations (it would be nice a bit warmer, too!).
Frank and Eileen
No longer RVers or FR owners