Take the belt off, turn it on, and give the pulley a spin in either direction. If it starts and runs quietly, and when you unplug it and it coasts to a stop you don't hear a Click, the centrifugal switch is probably stuck open. If you do hear a click, then probably either the starting capacitor is bad or the centrifugal switch contacts are burned or otherwise not making a connection.
So the fix is to lubricate and exercise the switch, replace the starting capacitor or burnish the switch contacts. Or maybe all three.