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Electrically, there needs to be a power source (battery), a complete current path (the wiring, switches (which includes the ECU), and connections), and the load (starter assembly and ignition system). There are so many interdependent components in a vehicle, the answer to your question is incomplete without including them. For instance, there also needs to exist a fuel delivery system, which sometimes includes electrical components - plus a myriad of mechanical systems and supporting electrical appliances.If you have a genuine interest in automotive systems and how they function, enroll in a community college auto curriculum.
If you use a magneto instead of a distributor you eliminate the ignition system. A magneto generates it's own power. If you have a manual transmission, it can be push started and eliminate the battery and starter. On a race car there would be no need for any electrical system, except a battery and starter so you wouldn't need a push start.