When a diesel is in "Wait to Start" mode, it is heating the engines' "glow plugs" before it tries to crank the engine. If your engine battery is low, then the typical diesel will not start.
Does your engine have a 110-VAC heater coil built in? If so, try to start your diesel generator, and then plug your engine heater coil into a receptacle. This will warm your engine block after a while. You should have some diesel status lights o your dash to tell you when things are OK to start.