If the social logins work but standard Joomla login does not, then it's not an issue with JFBConnect. The SCLogin module uses Joomla's own login functionality to authenticate the user. The SCLogin module is simply a different look to the standard Joomla mod_login module. The best test I'd recommend is to enable the standard Joomla mod_login module and test again. If it still fails, that absolutely indicates that it's not JFBConnect.
I hope that helps explain. From what you describe, our social authentication process and features are working, but if you find something different, please let us know and we'll gladly help investigate further.
Thanks,
Alex