Try this code out. I do not know your alternate menu image filenames
so you will need to change them from the dummy names in the "imgList" array.
It should work, but I cannot check this out without the filenames.
(Note: This also assumes all the menu images are in the same baseURL+imgPath directory)
Take out the testing code when you are happy with the results. 
<html>
<head>
<title>Katja de Vries - Home</title>
<link type="text/css" rel="stylesheet"
href="http://www.katjadevries.nl/css/desktop.css" media="screen" />
<script type="text/javascript"
src="http://www.katjadevries.nl/js/prototype.js"></script>
<script type="text/javascript"
src="http://www.katjadevries.nl/js/scriptaculous.js?load=effects,builder"></script>
<script type="text/javascript"
src="http://www.katjadevries.nl/js/lightbox.js"></script>
<script type="text/javascript">
// From: http://www.webdeveloper.com/forum/showthread.php?p=1188629#post1188629
var baseURL = 'http://www.katjadevries.nl/';
var imgPath = 'images/pl2/menukleur/';
var imgList = [
["menu1.jpg","menu1a.jpg","menu1b.jpg","menu1c.jpg","menu1d.jpg","menu1e.jpg"],
["menu2.jpg","menu2a.jpg","menu2b.jpg","menu2c.jpg","menu2d.jpg","menu2e.jpg"],
["menu3.jpg","menu3a.jpg","menu3b.jpg","menu3c.jpg","menu3d.jpg","menu3e.jpg"],
["menu4.jpg","menu4a.jpg","menu4b.jpg","menu4c.jpg","menu4d.jpg","menu4e.jpg"],
["menu5.jpg","menu5a.jpg","menu5b.jpg","menu5c.jpg","menu5d.jpg","menu5e.jpg"],
["menu6.jpg","menu6a.jpg","menu6b.jpg","menu6c.jpg","menu6d.jpg","menu6e.jpg"],
["menu7.jpg","menu7a.jpg","menu7b.jpg","menu7c.jpg","menu7d.jpg","menu7e.jpg"]
];
function randomMenu() {
var sel = document.getElementById('menu').getElementsByTagName('img');
var rnd = Math.floor(Math.random()*6); // 6 is number of alt image text for menu
// rnd = 0; // for testing purposes only
var str = ''; // for testing purposes only
for (var i=0; i<sel.length; i++) {
sel[i].src = baseURL+imgPath+imgList[i][rnd];
sel[i].alt = baseURL+imgPath+imgList[i][rnd];
sel[i].title = baseURL+imgPath+imgList[i][rnd];
str += '\n'+sel[i].alt; // for testing purposes only
}
alert('Menu #'+rnd+'\n'+str); // for testing purposes only
}
window.onload = function() { randomMenu(); }
</script>
<style type="text/css">
#menu.img { border:2px solid red; }
</style>
</head>
<body>
<div id="wrapper">
<div id="menu"><br />
<a href="http://www.katjadevries.nl/index.html"><img src="" alt="" title="" /></a>
<a href="http://www.katjadevries.nl/drawings.html"><img src="" alt="" title="" /></a>
<a href="http://www.katjadevries.nl/typo.html"><img src="" alt="" title="" /></a>
<a href="http://www.katjadevries.nl/photo.html"><img src="" alt="" title="" /></a>
<a href="http://www.katjadevries.nl/movies.html"><img src="" alt="" title="" /></a>
<a href="http://www.katjadevries.nl/other.html"><img src="" alt="" title="" /></a>
<a href="http://www.katjadevries.nl/contact.html"><img src="" alt="" title="" /></a>
</div>
<div id="largecolumn">
<img src="http://www.katjadevries.nl/images/boeken.jpg" />
<p>This website contains a selection of my work - old and new.
On your left you'll find the menu, which will guide you through the pages...
<br />You can click on each detail to see the whole picture, and get a description.
<p>You can always <a href="http://www.katjadevries.nl/contact.html">contact me</a></p>
</div>
</div>
</body>
</html>
Note also you have some errors in the external CSS code.
In particular, "backgroundcolor" probably should be "background-color"
There are some others if you look at the FF or Chrome error console.