On a car engine the battery is esentially only needed to start the engine. Once its started the alternator provides the 12V needed to operate everything. The generator doesn't have an alternator, it's just an engine turning a generator to make 120 VAC. It still needs 12 VDC for all its control circuits, fuel pump etc.
Bob Kulhanek 1995, 29 ft, Coachman Leprechaun, Ford E-350, EFI 460, 4.0 Onan Gen
If it won't budge, hit it harder or get a bigger hammer.