Philip,
I just tried to register on your site, and ran into a PHP error when trying to load the JFBCProfiles plugin for integration with Community Builder. Do you have Community Builder installed? If not, you should unpublish that plugin. Similarly, if you have the Agora, K2, JomSocial, or Kunena plugins published, but don't have those extensions installed, you should unpublish those as well.
Having that plugin enabled without Community Builder installed is likely what's causing your login issues, and hopefully, unpublishing it will fix you right up. If not, let us know!
Good luck,
Alex