Oh, that 583A crane (didn't recognize the number)! Its the Lionel reissue of the venerable AF crane. Assuming that no one has messed with it, it almost certainly is AC. As you likely know, this is set up so that rotating the crane cab also lifts the hook/magnet -- the cord is tied off on the stationary frame behind the rotating cab so as it rotates, that cord doesn't move, but simply raises/lowers the hook. One thing you might try is to untie the cord just to see if the cab rotates without it - perhaps the cord is binding on something. IIRC, you should be able to remove the cab and then see if the motor axle is spinning -- looking at it from below, you should be able to see the motor and gearing (well, you could on the old version - I suppose now its a can motor).
FWIW, I acquired an old 583 -- not sure, it might have been the -A version -- the difference is whether the controller is one button or two (not relevant for yours). In any event, I rebuilt mine using small Tamiya (I think) electric motors purchased from a robotics store so I have completely independent control of the raising/lowering of the hook/magnet and the right/left rotation -- all done through a simple joy stick. I can post pictures if anyone is interested.
