Norman,
Thanks for the link to your site. The problem is indeed another Facebook extension. While the Like buttons and other things may work normally, the Login button has to be setup very specifically, as authentication is a big security issue for Facebook. The other Facebook extension is initializing the Facebook library in a way that conflicts with JFBConnect (and is meant for a more 'basic' Facebook integration).
I'm not sure if this is from EasyBlog, or some other extension. If you open the HTML of the page you sent me, and do a search for "all.js", you need to unpublish whatever is inserting the 2nd block of code that you'll find that text in. The first block is from JFBConnect.
Once gone, logging in should start working fine. If it is EasyBlog, you simply need to figure out how to remove their inclusion of the Facebook API library. You can continue to use their Facebook Like buttons, or whatever they have, and you shouldn't have problems with those.
Hope that helps,
Alex