Well, you certainly have an old library. jQuery UI 1.10.4 is from January of 2014. And wasn't designed to work with the jQuery 3.x series (first released June, 2016). But that's not likely your problem.
But we can't tell from your header information what you actually have on your server, whether you have error messages on the Javascript console, what the differences are between your "test program" and "live program" or whether all the needed files are in fact present, or might be corrupted.
First step is to look for error messages in the Javascript console of any desktop browser.
Why are you using such an old JQUI library? Are you updating an old site? Did it once work, and stopped working correctly at some point? If so, when? What changed?