Sorry for the slow reply – busy preparing for a 4-week o'seas holiday!
Stratmando, I think you're possibly thinking of a 'universal' motor, with both stator (field) and rotor windings (with a commutator). That type of motor can be connected in series or parallel depending on the application and supply voltage. But Jim's motor is an induction motor, so it has no rotor winding, just a 'squirrel cage'. Have a look at
Single-phase induction motors : AC MOTORS for an explanation of how it works, though that site requires some engineering knowledge to fully understand. The explanation for a 3-phase induction motor (and the squirrel cage) is a few pages back from there. In all cases, an induction motor requires a rotating magnetic field (to start, at least), and for a motor operating on a single phase, a capacitor is used to generate a pseudo 2nd phase to generate the rotating field.
Jim, did you measure the two winding resistances, and are they equal? Secondly, are you running it on the rated 240V supply? In north America this would require a 2- or 3-phase supply to your house/workshop, so you could connect from one phase to another (which I think only gives you ~210V anyway), or a step-up transformer. In civilised countries

you would just connect from phase to neutral for 220 or 240V. Keep in mind that the torque available from the motor will vary as the square of the supply voltage, so if you tried to operate that motor on 120V, you'd only get 25% of its rated torque.
Note from the page linked above that some 2-phase motors have an extra capacitor switched-in during starting. Is there any chance yours is like that, and somehow the 'start' capacitor hasn't been correctly re-connected, or is faulty?
Daniel