If you're wondering what my guess was, here it is.
The torso and head LEDs are all one unit which the shoulders plug into. The signal that tells them what color and brightness to be (at least from what dad told me) travels something like this. Not quite sure about the head though so take that part with a grain of salt
My guess was that the signal got interrupted at the broken part because Dad's repairs were damaged during installation.
I was partly right about that last part, they were completely disconnected. As for the rest... I'm not sure