If you have an older 4K Onan like the KY series they work on a 'voltage in / voltage out' basis, if you put 12+ volts in, you will get 120 volts back out.
If the voltage in the house battery is below 12 volts though the output voltage would be too low and so the Onan just stops the output and shuts down. A battery as low as 9 volts will start that little engine, but isn't enough to operate the generator safely. Holding the start button bypasses the shutdown function.
If you have someone else to help you, try starting it with the chassis engine running and the emergency start button held down. The increased voltage from the chassis might just do the trick.