If it did not work previously it is possible the motor problem existed before you hooked it up.
I would dismantle the motor and check the condition of the windings and the centrifugal start switch.
You should have a capacitor mounted on the outside.
The lead to the centrifugal switch will also help you identify the start winding and then it should be easy to hook up as the other winding will be the run winding.
Al.
CNC, Mechatronics Integration and Custom Machine Design
“Logic will get you from A to B. Imagination will take you everywhere.”
Albert E.