Servis and other motors
That type of motor didn't use a start capacitor. There is a centrifugally operated switch at the 'wiring end' of the motor, operated by a weight and 'slipper' on the shaft. The contacts have probably burned (a common fault) or the shaft mounted assembly has broken down (less common, and characterised by the noise of something flying apart at 1440 rpm). Don't leave the motor energised for more than a few seconds in this condition, as the run winding will soon overheat (the motor is still effectively 'stalled'). Assuming the start winding hasn't burnt out (characterised by an obvious 'burnt' smell), the 'acid test' for a start switch fault is to get the shaft spinning by hand, then energise the motor. if it accelerates and runs, it's a faulty switch!! It may help to wind a bit of string around the pulley or shaft to provide a temporary 'pull-start', the faster you can spin it, the easier it will start. Obviously, if you ARE using a piece of string, make sure it fully unwound and off the shaft before hitting the power.
A single phase induction motor will run in either direction, so it doesn't matter which way you spin it.
All best
Dave T