Most jet engines are air start, where the APU bleed air is ducted to the engine and provides the motive force to crank the engine for starting. If APU air is not available then an external air source is needed, otherwise there is no start.
All turboprop engines that I am famiar with have DC electric starter motors, hence can start on ship's batteries, or with a ground power cart providing current, or the APU providing the current.
Some jet engines, such as the ALF502/LF507 also have electric starter motors. In this particular instance, 4 engines on a 146 can be started in a shorter time span than 2 engines on 737/717 types.
Again with the 146, BAe in their own inimitable style produced many variants that could not start an engine without either the APU or a DC ground cart. In the fleet I flew, there were two exceptions, both -300s. In these examples, one pilot had to exit his/her seat, open the hatch into the E&E bay, and press a switch that was recessed into the hatch opening. This would then allow an engine to be started on the ship's battery. The hatch would have to be replaced, lest the cabin crew disappear down into the E&E and the pilot would resume their seat.
I kid you not!
