Our cart has been thoroughly tested in a wide range of Web sites, design software, browsers and operating systems in every combination and found to work reliably and predictably. If there is a problem using the cart in your site, it is because of a conflict with something else you are doing in your site, so that would be up to you to troubleshoot and sort out.
I can point out that our cart is already based on a thickbox-style overlay and also uses jquery in some cases, so you might need to remove your thickbox and jquery script references or change the order in which they and our cart script are called in your source code.
If you could create a version of your page that has no other script references and only contains our cart code, then if that page is still having problems we can take a look. If that page does not have the problem, then you can start re-adding your other script references one at a time and Ctrl-reload your page in IE after each one until you find which one starts causing the problem as soon as it is introduced.
BTW, this is the complete block of our script-related cart code, which you should keep intact wherever you move it around in your page source:
<script language="javascript" type="text/javascript">
<!--
function EJEJC_lc(th) { return false; }
// -->
</script>
<script src='http://www.e-junkie.com/ecom/box.js' type='text/javascript'></script>