Hello,
I checked your site again and there are some problems.
1. you load jQuery and then turn it to noConflict mode. After it you load jQuery again and then Mootools. It is not problem of reported bug, but second load of jQuery is not necessary and maybe it can make some problems later. I am not sure.
2. Main problem is probably in your template. Exactly in component.php. Please open that file in:
templates/{template_name}/component.php
and check if there is <jdoc:include type="head" /> inside <head></head> tags. If no, then your popup window is without javascript functionality, so buttons can not work.
