Just three days ago I had to do work on a similar build-up nickelodeon
at the Musical Instrument Museum (MIM) in Phoenix.  As far as the
broken belt, I went down to the local Ace Hardware store and found an
"O" ring that is used on a water purifier that was 3/16" thick with an
inside diameter of 3.25".  It works beautifully.

I will not go into the logic for the coin mechanism since all of this
is by-passed with the continuous switch in the "On" position.  For your
motor problem I would first suspect the dimmer switch.  Some of these
dimmers have a push-On/push-Off operation which could be in the "Off"
position.  Check for this.  It should be easy to remove the dimmer from
the equation since it is connected using wire nuts.  Rewire it so power
goes directly to the motor.  Now, with the continuous switch "On", you
should be getting power to the motor.

It might be best to remove the cover on the quietizer box and see if
the wires leading into the box are connected to the motor.  I have seen
cases were the motor has rotated two or three times inside the box and
pulled one of the wires apart inside the box.  This happens because
when the motor starts up, the starting torque rotates the motor within
the case!  If everything looks good in the vacuum box, check for
voltages at the motor using a volt meter.

If none of these things solves your issue, replace the plug at the end
of the cord.

Pete Knobloch
Tempe, Arizona