Check the resistance between each pair of wires on the motor. If the motor is healthy you'll get the same resistance between any pair +/- 10% at most. (There's a total of 3 combinations to try). An open or short winding will give you a different reading. Motor windings are mostly much less than 1 ohm, so you need a meter able to measure low resistances for you to see any difference!
On delta wind motors, which most are, even a completely open winding only causes an increase in resistance (there is still a path between the other 2 windings), so 1 wire pair will give a reading double the other 2. That's why you need to be able to actually measure the resistance rather than just make a continuity check.
Even if the windings check out there are still some possible problems with the motor. Check that the motor spins freely with no grinding sounds (this checks bearings and for debris from an exploded armature). Also put light pressure on the end of the shaft and try to push it through the motor (but not too heavy handed!). Sometimes armatures come unglued from the motor shaft.