I do not know why this is happening but it looks like a CSS conflict.
First you need to use class="fancybox-inline" instead of class="fancybox" for the inline content (form) link. Then in your themes stylesheet give your body (or .body-class) element a height: 100% rule. For some obscure (to me) reason the body height does not get calculated correctly by the FancyBox script wich results in the popup being located always out of view. The 100% height style rule should fix that…
It’s working in Chrome & IE not Firefox. In both Chrome and IE when the form pops up, the bottom of the form is cut off and there’s no scroll bar.
I see a scroll bar in Chrome but you might want to disable the ‘Include Mousewheel jQuery extension’ option to prevent wheel scroll getting ‘caught’.
About Firefox, I see the issue remains the same there. Sadly, I have no idea why this is happening at all. The 100% height trick is the only solution I could come up with 🙁
