I added the img and bound a click handler using jQuery. So, when I disable everything else, I also unbind that click handler so the image button doesn't work anymore. Anyhow, here is an updated working example. I tested this in IE and FF. Let me know how it goes.
<!DOCTYPE html>
<html lang="en">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.3/jquery.min.js" type="text/javascript"></script>
<script type="text/javascript">
$(document).ready(function(){
$("button").click(function(event){
alert("you clicked the link, everything should be disabled now.");
$(".ui-datepicker-trigger").attr('disabled',true);
$("img.ui-datepicker-trigger").unbind('click');
});
// add a click handler for the img element
$("img.ui-datepicker-trigger").bind('click', function() {alert('clicked the img');});
});
</script>
</head>
<body>
<button class="ui-datepicker-trigger">Disable Everything</button>
<br/>
<input type="text" id="txt1" class="ui-datepicker-trigger" value="textbox 1"></input>
<img class="ui-datepicker-trigger" src="calendar.jpg" alt="..." title="..." style="display: inline;">
</body>
</html>