It sounds like you've already checked, but definitely make sure that the Joomla 1.6/1.7 versions of the component and plugins are installed.
Then, if it doesn't still work, try the following:
1) Disable any profile plugins (if any are enabled).
2) Go into the Configuration area of JFBConnect and simply hit "Apply". You don't need to change any settings, though you're free too.
3) Try re-enabling the profile plugins and hopefully you should be good to go.
If that doesn't fix it, instead of uninstalling any plugins, try disabling them in the Plugin Manager, and see if there are any circumstances that it does work with (no plugins enabled, etc).
Hopefully, the above steps are it, but if not, let us know.
Thanks,
Alex