Couple things you could try. All will require you to access PHPMyAdmin from your cPanel.
WARNING. Making changes this way could have a negative impact on your site, be sure to backup the database before performing ANY of these actions.
1 - Go to the bx_facebook_accounts table and change the profile ID for your account to 9999, this will remove the Facebook Connect from your account and require you to login manually.
2 - If that fails or your account is not linked to FB go to the sys_modules table and find the row with name "bx_facebook" and change the enabled flag from 1 to 0.
3 - If that fails, go back to the sys_modules table and find the row with name "bx_facebook" and change the pending_uninstall flag from 0 to 1.
Lastly, if all else fails. remove the row with the name "bx_facebook" from the sys_modules table and remove drop the bx_facebook_accounts table.
If none of these work I'm not sure what else could be the issue but would advise restoring the database from the backup to undo all the changes made above