Why won't my car start again if I shift from park to reverse while starting the engine?

Your car has an automatic transmission which includes a "neutral safety switch" to prevent the car being started while the shifter is in any position except "neutral" or "park". This switch is activated by the shift lever and prevents voltage to the starter solenoid when the car is in gear (drive or reverse). This is a safety features that prevents the car from lurching ahead or backward while starting.