You need to get completely away from any preconception of the engine and drop it down to the minimum.
As I stated before the pistons and crankshaft are a must, although someone might go further and remove the crank, but I really would think that this is taking projection of the design beyond reasonable limits.
Storage has to be electrical, as the remit is no starter motor, any external rotational device would by default have to be discounted, otherwise One would just be using a different pattern of starter motor.
Compressed air is an interesting possibility, but it would have to be applied to a flywheel/ turbine combination and thus not too far removed from a starter motor. Or it would have to be introduced to the cylinders in a timed fashion, in which case, One is better to go the whole hog and add the fuel and spark as well. The only logical conclusion to this is individually acting mechanically isolated valves and injectors along with spark generators and linear transducers to provide the precise positional feedback of valves.
Temperature, fuel, air mix and needless to say the crank position would need to be defined also, although there is an argument that to make life almost liveable for your AA patrol man, each piston would need it's position defining.
Best not to think in terms of an ECU incidentally, it encourages entry into the rut.
Try CPU instead :-)
AB