Mark, it should be fairly simple to determine what is going on here but AMI's odd stereo setup can confuse a bit.
First, the center speaker is the 12in woofer and on AMI's is is wired mono and draws power from both channels (assuming you have a stereo amp).
This first requires that the pickup be wired -out of phase-. If the pickup was replaced by someone who didn't understand what is going on, they may wire it the conventional way and thus both channels will cancel although you would still get at least some sound (mostly distortion) from the center.
From what I recall the speaker package on this machine merges to an Amphenol-type plug and these can become erratic so (if that is what is used) try wiggling the plug while music is playing and see if the center come on.
If you have sound from both side speakers chances are that both channels are working. However given that we are talking about jukeboxes and what people do to them, I'd trace out the side speaker wires to be sure that they are each actually connected to separate channels and not the same one.
Finally, you'll need to track down the woofer leads. These emerge from behind a removable access panel which is behind the amp. Just two wires -shouldn't be hard to find. IIRC They are the usual black and red. Try giving them an ohmmeter test. The speaker is 16 ohm and thus should read about 12 ohm on a meter.
http://www.verntisdale.com/AMIschem.htm -Has schematics
Rob/NYC