Hi sitemakiyato, there are several thing going wrong:
1. your theme seems to be loading a very old jQuery version on its own on top of the one included with WordPress. I see this just before the closing </head>
tag in your page source code:
<script type="text/javascript" src="https://ajax.googleapis.com/ajax/libs/jquery/1.4.4/jquery.min.js"></script>
This needs to be removed. If you want to use a Google hosted jQuery, then use the plugin Use Google Libraries https://www.ads-software.com/plugins/use-google-libraries/
2. your theme is missing its footer.php (probably) or somehting is preventing proper execution. This causes the page source code to be incomplete and missing the proper script files for FancyBox and probably other stuff to run. You need to find out why this is happening.
A look in the error log files might help. Or disable all plugins, check if the footer is properly working then, and then enable each plugin one by one until you find out which one is causing this…