Testing if jQueryUI has loaded

if (jQuery.ui) {
  // UI loaded
}

OR

if (typeof jQuery.ui != 'undefined') {
  // UI loaded
}

Should do the trick

You need to check if both, the jQuery UI Library file and CSS Theme are being loaded.

jQuery UI creates properties on the jQuery object, you could check:

jQuery.ui
jQuery.ui.version

To check if the necessary CSS file(s) are loaded, I would recommend you to use Firebug, and look for the theme files on the CSS tab.

I've seen problems before, when users load correctly the jQuery UI library but the CSS theme is missing.

Just test for the ui object, e.g.

<script src="jquery.js"></script>
<script src="jquery-ui.js"></script>
<script>
  $(function(){
    // did the UI load?
    console.log(jQuery.ui);
  });
</script>

You can check if jQuery UI is loaded or not by many ways such as:

if (typeof jQuery.ui == 'undefined') {
   // jQuery UI IS NOT loaded, do stuff here.
}

OR

if (typeof jQuery.ui != 'function') {
    // jQuery UI IS NOT loaded, do stuff here.
}

OR

if (jQuery.ui) {
    // This will throw an error in STRICT MODE if jQuery UI is not loaded, so don't use if using strict mode
    alert("jquery UI is loaded");
} else {
    alert("Not loaded");
}