Very good.
Guess I misinterpreted the noise. When the cap goes the motor won't even start. It's called a starting capacitor. It is in series with a centrifugal switch that connects a starting winding in the motor, the cap and the switch when the rotor isn't turning. Once the thing hits a certain speed the switch opens and the circuit isn't needed. It the cap fails open then there is a low level hum. If it shorts then there is a louder hum. In either case, no start. FYI another failure mechanism that has been posted as a problem many times is the switch contacts get dirty and they won't close. Just remember this for now. Usually a very simple and cheap fix.
Al