Hmmm. Very strange. I investigated a little more as to what could be happening by analyzing the output HTML. It seems like something on your site is preventing the onAfterRender system call from occurring. onAfterRender should be triggered on all system plugins, and that's where JFBConnect replaces the Easy Tags with the proper HTML. It's also where some specific Javascript files are loaded for Facebook (and other social networks) integration.
When I look at the HTML output on your page, I see the following things that aren't executing properly from our system plugin:
* The raw easy-tags
* Our 'placeholder' tags, like :
<JFBConnectSCTwitterJSPlaceholder />
<JFBConnectSCGooglePlusOneJSPlaceholder />
<JFBConnectSCPinterestJSPlaceholder />
<JLinkedJfbcJSPlaceholder />
Our system plugins are definitely enabled, because I can see other functions that they perform in your code.
I'd scour your plugins and extensions (or any modifications you've made to Joomla core files) to see if there's anything that would be trying to aggressively 'optimize' the site by removing function calls, specifically the onAfterRender routines. I really don't have any great suggestions as to where to start, but you'll need to narrow down what's preventing basic Joomla functionality from triggering.
I hope that helps,
Alex