There's a few reasons that can cause the Login button to not work. Can you first make sure that Autotune has correctly configured your Facebook Application and that no errors are returned in the Error Checker test. If that all passes, let us know what version of JFBConnect you're using so we can help diagnose things a little more.
Finally, please post from the account you subscribed to JFBConnect from. Priority support is for active subscribers only.
Thanks,
Alex