I just thought of something else that can cause this, which we experienced a few months ago. In the layout.master of the skin, there is a key for Stylesheetcombiner that looks something like this:
<portal:StyleSheetCombiner ID="StyleSheetCombiner" runat="server" UseArtisteer3="true"
JQueryUIThemeName="smoothness" UseIconsForAdminLinks="false" UseTextLinksForFeatureSettings="false" />
If JQueryUIThemeName is set to "base", you'll need to change that to "smoothness" or another allowed value. For some reason, the JQueryUI team removed "base" as an allowed theme name, and if you use it then JQueryUI will not load.
I hope that helps,