It appears you have the main Fancybox .js file linked to from the <head> of your page, but I don't see the following in the <head> anywhere (though I might have missed it):
/* This is basic - uses default settings */
/* Using custom settings */
/* Apply fancybox to multiple items */
'transitionIn' : 'elastic',
'transitionOut' : 'elastic',
'speedIn' : 600,
'speedOut' : 200,
'overlayShow' : false
Then on a linked image (if it's just a single image that's not part of a group) than it needs an ID (you can only declare an ID once per page) of single_image:
<a id="single_image" title="" href=""><img src="" alt="" /></a>
If you have a group of images (as it appears you do on that page) you can assign a class (can have as many of the same class as you want per page) of grouped_elements with a matching rel="" attribute.
<li><a class="grouped_elements" rel="group1" href="#" title="#"><img src="image1.jpg" alt="" /></a></li>
<li><a class="grouped_elements" rel="group1" href="#" title="#"><img src="image2.jpg" alt="" /></a></li>
Also you appear to be using an older version of Fancybox. Not sure if upgrading to the latest will solve the issues you're having, but it's probably a good idea to do, nonetheless.
Hope it helps.