The FullCalendar package comes with jQuery v1.3.2, whereas the latest version of jQuery is 1.4.2. It also uses jQuery UI core, resizable and draggable v1.7.2 (not Modal), and the latest for these files would be 1.8.1.
So, I don't know which versions you are using, but I do know that FullCalendar works with jQuery v1.4.2 because it is working on one of my sites (I still have jQuery UI 1.7.2 running). So first off, check to make sure each plugin works with your files separately, then together.
Also, it would be a good idea to get the Firebug addon (Firebug lite for non-Firefox browsers) to show you if any errors are occurring.
Edit: You could just link to the Google API versions of jQuery/jQuery UI
<script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.4.2/jquery.min.js"></script>
<script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jqueryui/1.8.1/jquery-ui.min.js"></script>
<link rel="stylesheet" href="http://ajax.googleapis.com/ajax/libs/jqueryui/1.8.1/themes/base/jquery-ui.css" type="text/css" />