Erratic motor start

My pump motor is new (second one). Sometimes it will start, sometimes not. I have tested voltage and amps. I then tested with pump removed. When I try to start it, it will sometimes start, sometimes the shaft will bump a tiny bit, sometimes not move. I have rotated the shaft manually and marked it to see if the position has an effect.  Does not matter. After it starts, I can turn it off and back on, and again, it may or may not start. I can turn the shaft with my fingers so it is moving freely. I can hear the relays kicking on in the control box. I have swicthed the wiring from  the booster pump to the main pump and still have the same problem. The only thing I have not switched is the actual wiring but it reads 120 V at both leads at the motor and the ground checks good. I have no idea what else to check.