Sounds like a fuel delivery issue. Specifically, a priming issue. Does your indoor switches have the "prime" position? (On many of the Onans, you can push it towards the "OFF" position and hold it for around 10 seconds to prime fuel into the carb bowl before engaging the starter.) Reason I ask, is that my unit does NOT have that feature on the inside switch. It is a simple momentary rocker switch. It primes from the engine turning over. The switch on the genset itself will push towards the "OFF" position, but doesn't activate the fuel pump. I have to hold the choke until it pulls enough fuel in.
Try cold starting the genset from the switch on the genset itself first. If it is hard starting from there when it's cold, then I can't see any problem with the inside switches. Once the genset is "warm", there's already fuel in the carb bowl and it should start right up. When it's cold, the fuel in the bowl has likely evaporated and unless you can prime it, it takes several cycles of the engine turning over to pull fuel into the bowl to inject into the carb for combustion. I suspect, it starts right up from the genset switch because you've already primed it enough from turning the engine over when attempting to start it from the inside.
