thanks for your post, and sorry for the trouble.
This is one of the more tricky things.
The main JS file of your theme wants to initialize the Fancybox Gallery JS script. This Fancybox scripts, in one line of its code, needs to find out what browser the viewer is using. For that, it uses the jQuery JS library. Your site is configured so that it will always load the latest version of jQuery library from the Google CDN network. And just a few days ago, jQuery was released in version 1.9, which (on purpose) drops support for the functionality to determine what browser the viewer is using.
So, because of that, the Fancybox script fails, and that causes the theme's JS code to fail. And that again stops all JS on the page, so that the sorting/search/pagination JS for tables also is not executed.
The mid-term solution is that the Fancybox plugin will need to update its JS code, so that it is compatible with jQuery 1.9. The short-term solution is to not load the latest version of jQuery from the Google CDN, but to use the version 1.8.3 that ships with WordPress. (This is probably done by your theme or another plugin that you have installed for this purpose.)
P.S.: By the way: WP-Table Reloaded has been replaced by a much better and official successor: TablePress. No immediate action is necessary (and this will not directly help with your issue), but I recommend that you switch in the next couple of months. For more information, please see http://tobias.baethge.com/2013/01/tablepress-replaces-wp-table-reloaded/