In Firefox, can you go to Tools -> Developer -> Web Console and then try to click the Facebook button. If any Javascript errors show in the console, let us know what they are.
Beyond that, my only suggestion is to try on a different computer. If you have a "Security Suite" on your computer or specific addons for your browser to enhance privacy, they may be blocking the communication with Facebook or the popup that should be showing.
Not sure what's happening there, but we were definitely able to login without any issue.
I hope that helps, but keep us posted on what you find.
Thanks,
Alex