Motor doesn't turn but makes noise
If you disconnect the capacitor, the motor will not start by itself. The capacitor is connected in series with one of the windings to give the motor a "second phase." All single-phase motors have some feature like that to allow them to start by themselves in the proper direction. It might start if you give the shaft a turn to assist it. If you put the motor back together and turn the shaft with the power off, it should turn freely. If it doesn't, it is misaligned or has some other mechanical problem.