Hi Paul,
By opening up the javascript console in Chrome, I was able to find this error in jquery.jcarousel.min.js line 16.
Uncaught TypeError: Cannot read property 'safari' of undefined
The file is minified, so it’s difficult to understand the problem. Can you give more information? Did it stop suddenly or did you recently change the site? Add a plugin or upgrade?
A quick search on google revealed this page:
https://github.com/jsor/jcarousel/issues/469
The plugin seems to be 18 months out of date and is need of an update. I would follow these instructions or perhaps find a newer/better carousel plugin.
http://wordpress.org/support/topic/the-plugin-does-not-work-under-wp-361?replies=3
Hope this helps!
Just to let you all know, a kind developer patched the plugin five months ago.
His blog post (http://www.letswoolgather.com/sponsors-carousel-patch-wordpress-plugins/) teaches you how to fix the plugin to work with wordpress 3.5 and above, but also provides a downloadable .zip file at the end of the post.
I highly recommend it!