Most of these motors are capacitor start only, once you have any kind of rpm the capacitor is out of circuit via the centrifugal switch, this just leaves the run winding across the supply.
The capacitor should have come with the motor?
Did you try connecting it direct to the supply, and bypass the rev. switch?
Have you identified the two circuits, the run winding and the cap-start winding?
Is the new motor dual voltage?
Al.
CNC, Mechatronics Integration and Custom Machine Design
“Logic will get you from A to B. Imagination will take you everywhere.”
Albert E.