Actually the fact that the Classic Slider works on a page and not working on another page shows that the problem must be something outside the slider itself.
To make sure what is the problem cause I suggest that you do the test below:
Add a new page and only add the Classic Slider that has a problem. Check the case and see if it is working ok. If yes then there should be some code or element in the page that you included the slider which causes the problem and you need to check that by adding a template of the page using the template manager:
Then add a new page and load the template to the new page. Then try to remove other sections of the page one by one and check if the slider works ok. Continue the task to find the section which is responsible for the conflict.