I don't know if this will be a help to you or not.
If the Fuji Finepix S1500 Mode Dial assembly is similar to the one in the Fuji Finepix S1600 then it may be.
Here are some images taken from the Fuji Finepix S1500 service manual showing the Top Cover parts and the electrical parts list for the camera.
(click on images to enlarge for better viewing)
Here is a link to the service manual where the images came from.
To download the file, when the sentence below the Document preview box changes from This file is downloadable free of charge: ...processing... to This file is downloadable free of charge: Get Manual, click on the Get Manual as this is the download link. Be patient, it takes a little while to find the file.
As I am not quite sure which part you mean, hopefully you can identify it and then search online for it using the title of the part or the part number from the manual.