Why don't you try to give the full url of all the css and js files.
From the example you uploaded it looks like your Shadowbox build is using the Jquery adaptor but you haven't included JQuery on your test page. Either include JQuery before the reference to shadowbox or download the standalone version of Shadowbox if you aren't using Jquery on your site.
I stumbled upon this forum when my shadowbox STOPPED working on one of my wordpress sites.
I had Shadowbox running on my 3 nearly identical Wordpress blogs.
Upon close source code inspection for differences as well as bits in this forum thread,
I finally found a difference.
2 Working blogs had Shadowbox 22.214.171.124 installed, whereas the broken blog had 126.96.36.199
I haven't logged in to the 3rd one often enough and missed the auto-update before the Shadowbox was pulled from Wordpress repository.
So I grabbed the latest version from the author's website, uninstalled the old, installed the new, and it worked. Easy.