You can now get to most of the stuff that breaks. Look for stuck gears and broken off wires.
If you need to get to the bottom of the stage, that is harder. You'll need to get down there if the figures aren't turning, or if there is a problem with the power switch/plug or volume control knob.
To get to the bottom of the stage:
Here is what the bottom of the stage looks like in case you are curious. That wire powers the motor that turns the dancers.
Update from Chris Lawrence 12/3/2023:
I did find an easier way to get to the base without having to worry about enough slack in the wires...
Q: Why?
A: My kids love these things, but they break. After my 3rd dead one, I decided
to give up on replacement and turn to repair. I looked all over the internet for
instructions on how to open the thing but found nothing. It took some time to
figure out how to do it, so I want to save the next person from wasting the time
I already spent.
12/17/2011: First published
12/3/2023 : Added Chris's new tips