I have no clue as to the type of pump you have, but it most likely is not the impellor, sounds like it's not getting enough amperage to start - if you don't have a trouble shooting manual, google and call the manufacturer for help. Sounds like it may be the capacitor which may or may not be built into the motor.

Depeding on how old the pump and it's cost, a replacement may be the better value in the long run. The comfort value of a new pump may have some merit to you.

Thank you