Hi, thank you for contacting JustAnswer.com. My name is Russell. I will do my best to provide the right answer to your question.
It's always right to run an old classic or antique device through all its functions before buying it... unless you just simply have to buy it period, I guess.
As for the stuck component 'on the track' - I don't know quite what you are referencing. Perhaps the selector arm?
Selector arms, and other moving parts in a jukebox, can become jammed. That you couldn't move it by hand rather suggests that.
On the other hand, without knowing what part it is that does not move, I can't be quite sure what I'm advising you about. So please describe the part that isn't moving, and I'll advise you further.
Selector arms can have defective actuators, or they can be jammed, or bent so that they are jammed, or rarer problems. Generally, for a really classic or really old jukebox, it's a good idea to clean and lubricate moving parts after a dozen years or so (or more frequently if the environment is damp. Are there any signs of corrosion or rust inside the case?)
As for the loose wire - describe where it comes from. Trace it to wherever the other end is connected... the best way of telling 'what wire it is' at this point. Also, is it obviously broken off at the free end? if the end is not capped nor taped, then it probably came loose or was broken or (doubtfully) was cut, even if the end has no obvious wire showing.
Let me know more about the problem, and what you find out by what I have recommended. Thanks.