Please go into the Joomla Global Configuration and set Error Reproting to "Maximum" and disable GZip compression. Then, try to recreate the white page error. That will hopefully display a pretty PHP message that will help narrow things down.
If that doesn't, I'd recommend disabling your JFBConnect Profile and Open Graph plugins and try again. If that works, slowly enable each plugin and test again so until you narrow down what plugin (if any) is causing the problem. Let us know, and we can definitely help from there.
Also, try with a different Facebook account to make sure it's not something specific to that Facebook user.
Thanks,
Alex