I just downloaded jQuery UI Tabs.  In the included index.html file, it works fine, CSS and all, with no customization.  I copied the files over to my web server, keeping the directory structure intact, and copied the content code to my already-existing index.html, but it does not work.
My Header Code
<script type="text/javascript" src="js/jquery-1.4.2.min.js"></script>
<link type="text/css" href="css/start/jquery-ui-1.8.custom.css" rel="stylesheet" /> 
<script type="text/javascript" src="js/jquery-ui-1.8.custom.min.js"></script>
<script type="text/javascript">
$(function(){
// Tabs
$('#tabs').tabs();              
});
</script>
My Body Code
    <div id="tabs">
        <ul>
            <li><a href="#tabs-1">First</a></li>
            <li><a href="#tabs-2">Second</a></li>
            <li><a href="#tabs-3">Third</a></li>
        </ul>
        <div id="tabs-1">Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.</div>
        <div id="tabs-2">Phasellus mattis tincidunt nibh. Cras orci urna, blandit id, pretium vel, aliquet ornare, felis. Maecenas scelerisque sem non nisl. Fusce sed lorem in enim dictum bibendum.</div>
        <div id="tabs-3">Nam dui erat, auctor a, dignissim quis, sollicitudin eu, felis. Pellentesque nisi urna, interdum eget, sagittis et, consequat vestibulum, lacus. Mauris porttitor ullamcorper augue.</div>
    </div>
My Output
* First
* Second
* Third
  
  Lorem ipsum dolor sit amet,
  consectetur adipisicing elit, sed do
  eiusmod tempor incididunt ut labore et
  dolore magna aliqua. Ut enim ad minim
  veniam, quis nostrud exercitation
  ullamco laboris nisi ut aliquip ex ea
  commodo consequat. Phasellus mattis
  tincidunt nibh. Cras orci urna,
  blandit id, pretium vel, aliquet
  ornare, felis. Maecenas scelerisque
  sem non nisl. Fusce sed lorem in enim
  dictum bibendum. Nam dui erat, auctor
  a, dignissim quis, sollicitudin eu,
  felis. Pellentesque nisi urna,
  interdum eget, sagittis et, consequat
  vestibulum, lacus. Mauris porttitor
  ullamcorper augue.
All of the files are referenced correctly, and it is all copied and pasted directly from a fully functional file., but it will not work.