I'm not real good at AC motors, but it sounds to me like the starter is screwed up. There's a ring with contacts that provides power to start the motor turning. As the RPM builds, this ring pulls away and the motor runs like any other ac motor. They use starters like that on compressors where there's a high load (the pump under pressure) that the motor has to turn as it starts.
Look at youtube and I'm sure there's some DIY videos on rebuilding AC motors. Do yourself a big favor and find out how to discharge the capacitors so you don't get knocked on your butt.
BTW, there are no brushes in this type of motor.
Depending on how big the motor is and its quality (read country of origin) you may just want to buy a new motor.