Alright.. didn't find a solution. Did notice that the popup works on other JomSocial pages, just not the main home page (Resend Activation, user profile pages, etc, work). On that home page, there's a Javascript error with the modal.js file right when the page loads, indicating some other Javascript code is 'attaching' to it in an incorrect manner.
The only real difference I can see on the JomSocial home page is that image scroller at the top. Can you try (temporarily) disabling that, and let me know if it works? Obviously, that's not a solution, but if it works, that will help us figure out the conflict.
Once done with that, disable the login popup for now, and we'll have to look into it further.
Thanks,
Alex