Tripped me up for a whole day this one. We have a number of content editor web parts on our intranet home page. One was working, three others that used the jquery ui were not.
I checked that all the paths to the js and css files were there and valid. All OK (excepting that we hadn’t copied the jquery.min.js file into the layouts folder).
I converted each to files, added the html back in and then linked to the newly uploaded file. All good.