The page you linked to is restricted, so I can't see the issue. I tried to register with Facebook, but I get the following message:
URL Blocked: This redirect failed because the redirect URI is not whitelisted in the app’s Client OAuth Settings. Make sure Client and Web OAuth Login are on and add all your app domains as Valid OAuth Redirect URIs.
Twitter brings me to a red page with "0 - Bad request token!". That is usually caused by having the Twitter app setup incorrectly. I'd recommend checking out the
Twitter Setup Guide
and making sure the Callback URL is setup properly in your app.
I couldn't find a way to register otherwise on your site, and can't see the page without logging in. Once you get that going, let me know and I'll gladly help however I can.
As for the actual issue, can you let me know what's happening to the social buttons in the stories that pop in? Are the social buttons just missing or are the raw JFBConnect tags just showing?
Any details you can provide will help us understand ahead of time before we see the issue when we login.
Thanks,
Alex