Dolly,
Do you have any JFBConnect profile plugins installed?
If not, can you try enabling the "Skip Joomla Activation" setting in the configuration area? Not sure why the user wouldn't be confirmed, unless it's configured that way, somewhere.
Finally, what are your settings for "New User Creation": Full Joomla User or Facebook Only? If Full Joomla, you have to create a username and password to login with.. if you do that, can you log in just through Joomla, or does that fail too?
Let us know, and we'll get you going,
Alex