I’ve been looking at the site for an hour or so and haven’t noticed any problems with the widget slider.
When the slider stops working it is typically a problem with jQuery. Sometimes when you update to a new version of WordPress the jQuery version used by WordPress is also updated. Any plugin that uses jQuery can cause it to stop running and you would see the testimonial widget slider stop working.
To troubleshoot (If the problem re-occurs):
1)De-activate all plugins except Testimonial-basics. DO NOT DELETE THEM….just de-activate them.
2)Check to see if Testimonial Basics is now working properly.
3)If it is working properly, then reactivate the plugins one at a time, checking the testimonial display each time until you find the problem plugin.
4)Once you find the plugin that is causing the problem, you can look for a replacement.
5)Let me now if you found a plugin and which one it is so I may take a look at it.
That said I dug a little deeper and noticed a few things. It looks like you have 2 versions of jQuery and jQuery UI being loaded….not a good practice. Version 1.7.2 of jQuery is being loaded from the World Village plugin and 1.11.0 from WordPress.
Plugins or Themes should not load their own jQuery files or jQuery UI files, but use the latest files supplied by WordPress.
I also ran a HTML check on a few pages, and have noticed quite a few errors (25-50). A CSS check shows over 400 errors in the css files loaded. Though I doubt these are the problems, they should be cleaned up.
I am also a bit puzzled about the Testimonial page. You have re-activated the plugin yet the Testimonial Basics Shortcodes are not executing?