The way the SCLogin module popup works is to append the popup area into the output of the main component on the page. The div is called "login-modal" and is hidden. When the button is clicked, the popup will appear.
On your page, I'm not seeing our hidden div in the component area output, which would explain why the popup doesn't work.. there's nothing to popup.
Can you try switching to a different template to see if it works? That will help narrow down if it's a template issue or something else.
Do you know if your site has anything to handle component output differently than most sites? Our popup mode works on many, many sites so far, so we just need to narrow down what's different about yours.
Thanks,
Alex