Would the automatic transmission not working stop car from starting?

No, an automatic transmission that is not working should not prevent a car from starting. The starter motor is responsible for starting the engine, and it is not directly connected to the transmission. In fact, cars with a manual transmission can be started even if the transmission is in gear, as long as the clutch is disengaged.

That said, a malfunctioning automatic transmission could prevent the car from moving, even if the engine is able to start. This is because the automatic transmission uses hydraulic pressure to engage and disengage gears, and if this pressure is lost or insufficient, the gears will not be able to change. Therefore, while a non-functioning automatic transmission will not keep a car from starting, it will keep it from going anywhere.