Continuing the discussion from JQuery accordion puzzle in quirks mode:
It could be that the jQuery you are using is not suited to IE6. The following is recommended for older versions of IE.
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.11.3/jquery.min.js"></script>
As an alternative I have re-worked your example using generic Javascript that does work in all IE from IE6 onwards. It is pasted below. I have placed the onclick handlers into the html so that you can see clearly how they work. I have also added the style.display attribute to the nodes that will be toggled to allow them to be tested by the script without needing to initialise on loading.
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html>
<head>
<meta name="GENERATOR" content="Microsoft FrontPage 5.0">
<meta http-equiv="Content-Type" content="text/html; charset=windows-1252">
<title>Toggle</title>
<style type="text/css">
body { font-family:arial, helvetica, sans-serif; font-weight:normal; font-size:14px; color:#000; text-align:left; }
#nav { width:300px; margin-left:20px; padding:10px; border:1px solid #CCC; }
h3 { font-size:16px; font-weight:bold; }
h3.tog { cursor:pointer; color:#00F; text-decoration:underline; background-image:url('scripts-img/16-arrow-down.gif'); background-position: right top; background-repeat:no-repeat }
ul.menu a { color:#F00; }
</style>
</head>
<body>
<div id="nav">
<h3>Leadership and Management</h3>
<h3 class="tog" onclick="togg('div1',this)">Functional Academies</h3>
<div id="div1" style="display:none">
<ul class="menu">
<li><a href="#">Audit</a></li>
<li><a href="#">Communications</a></li>
<li><a href="#">Finance</a></li>
</ul>
</div>
<!-- end div1 -->
<h3 class="tog" onclick="togg('div2',this)">Other Divisional Academies</h3>
<div id="div2" style="display:none">
<ul class="menu">
<li><a href="#">Group Operations</a></li>
<li><a href="#">Insurance</a></li>
</ul>
</div>
<!-- end div2 -->
</div>
<!-- end nav -->
<script type="text/javascript">
var openObj=[]; // global
function togg(ref,clickedObj)
{ var refObj=document.getElementById(ref);
// check if already open and close it
if(typeof openObj[0] !="undefined" && openObj[0] !=refObj)
{ openObj[1].style.backgroundImage="url('scripts-img/16-arrow-down.gif')";
openObj[0].style.display="none";
}
// toggle clicked object
var result=(refObj.style.display=="none")? ["block","16-arrow-up.png"] : ["none","16-arrow-down.gif"];
refObj.style.display=result[0];
clickedObj.style.backgroundImage="url('scripts-img/"+result[1]+"')";
// set refs to current open object
openObj=[refObj,clickedObj];
}
</script>
</body>
</html>