Without looking at a wiring schematic or knowing right off how they excite the start up circuit, I will just throw this out there as just by chance it may help you. It wont hurt you but it may help.
With the gen running lug in an electric drill motor a hold the trigger on and spin the drill motor by hand. I have done that trick on portable units that have lost their residual magnetism in the rotor. Yours has not sat long enough for that to happen normally. It normally happens on units that have sat a long time. It's worth a try but dont hurt yourself or wrap your shirt sleeve up if it takes off.