A common reason for pumps not starting is failure of the start capacitor. There can be two types of capacitors in a pump - a start capacitor and/or a run capacitor.
Not all motors have run capacitors. The newer VS pumps do not have a start capacitor either.
The start capacitor is often under the small bump at the top of the motor. Or it can be inside the motor.
Some capacitors have a bleed resistor connecting the two prongs. If your capacitor has a bleed resistor it should be moved to the new capacitor.[1]
Be careful when handling a capacitor. It can hold a voltage charge for a long time and you can be shocked by it.
