Can you verify that the following file exists, is readable, and has something in it? Mainly, at the top, there should be a reference to "class JFBConnectModelConfig".
/administrator/components/com_jfbconnect/models/config.php
If that file is missing, then the installation of JFBConnect is really messed up for some reason, and you'll need to copy the files like I mention. Beyond that, the only reason the file above that is throwing the fatal error is loaded is if the JFBCSystem plugin is enabled. If that's disabled in the database tables, like I mentioned, JFBConnect won't load or do anything when you access the admin area.
So, with one of those, you should definitely be able to access at least the admin area. If not, then some other piece of code is trying to load our library... normally, that should be fine too, but obviously, something's going wrong on your site.
Hope that helps,
Alex