More than likely the extra wire is for the start windings. Most ac motors rely on an additional set of windings to get the motor spinning in the correct direction. This can be accomplished several different ways, Most larger motors, will use a starting capacitor or a capactior and relay combo. Some, like most bench grinders, have a switch that closes and opens based on motor rpm. It is real common for the capacitors to fail. You may want to look for it and see if it looks burnt. If you can spin the motor by hand and get it to turn it is most likely a start circuit issue. The tip off to this is the motor will generally just hum but if you give it a flip it will work fine until turned off.
If you do need a motor, there are usually lots of places that will either repair of seel you a replacement