Hi, I would first check the lock nut and set screw on the bottom of the cannon mech. If it has come loose or was not tightened properly the motor will actuate but the cannon will just sit there as the shaft is spinning in the mount.
If your motor is not working check to make sure it is not siezed or smells like it has burned. Then check the fuse in the back cabinet or possibly under the playfield that runs inline with the motor. Check your wires for breaks. Also make sure the proper rated fuse was installed by the previous owner. If none of these problem exist I would then suspect a possible faulty diode or transistor for the motor circuit or possibly a broken loose wire. If you do not have a manual check the internet pinball database, a PDF of it is there.
If you are really stuck or can't figure out the scematics send me a message and I will look over the wiring diagram and let you know what transistor # runs the motor and the plug locations/wire colours so you can test it. You are going to have to get a multimeter if you don't already own one.
Good luck hopefully its a simple fix.