for short periods, 240VAC will not burn out a 220VAC motor. furthermore, switching the polarity of the wires will not blow up the motor. here are the things to check:
to begin with, disconnect the 240 VAC power and apply an ohmmeter to the SAME motor terminals to which you had applied the 240VAC power. your ohmmeter should read almost ZERO ohms. If it reads high ohms, either the windings of the motor are burnt open (throw the motor away) OR the terminals you chose are not those used to power the motor.
How can this be? in a single-phase motor, two of the wire terminals leading to the motor go to the stator winding and the third terminal (the green ground wire) is connected to the motor housing. connecting one of the 240VAC leads to one of the stator terminals and the other to ground will not power up the motor.
furthermore, in a single-phase motor there is a switch which temporarily patches in a capacitor (the start capacitor) which furnishes a phase lag to one set of stator coils in order to get the motor to start from zero RPM and spin up to speed, after which the capacitor is patched out of the circuit. if this switch is bad, applying power to the motor terminals will not start the motor. If your motor is of the "capacitor-start" type and it won't start, you must check the proper operation of the start switch as well.