1) Make sure you don't have other Facebook extensions installed. Mainly, check the HTML on the page and search for "all.js". It should be there only once.
2) Check that the following page loads properly (it should be just blank, but if you look at the HTML, it's loading a Javascript file):
site.com/components/com_jfbconnect/assets/jfbcchannel.php
If you get an error, check the existence of, and permissions on, that file.
3) If it's still not working, then it's likely a Javascript error on the page: Turn on the "Display a notification about every error" setting in IE and check again. Even JS errors from other extensions can conflict with Facebook's JS library.
Hope that helps,
Alex