Well, one thing I notice is that there is strange stuff in your source code. Your site says you are using 3.7.1, but the javascript you are calling in your page is for 3.6.8 - look for the ".js?v=368" at the end of all the javascript calls on that page - examples:
Code:
<script type="text/javascript" src="/yahoo-dom-event/yahoo-dom-event.js?v=368"></script>
<script type="text/javascript" src="/connection/connection-min.js?v=368"></script>
These are the lines in the headinclude template (that relate to those two):
Code:
<script type="text/javascript" src="$stylevar[yuipath]/yahoo-dom-event/yahoo-dom-event.js?v=$vboptions[simpleversion]"></script>
<script type="text/javascript" src="$stylevar[yuipath]/connection/connection-min.js?v=$vboptions[simpleversion]"></script>
And, none of your security tokens are getting made either. My guess is this is all related. Are you sure you ran the upgrade script successfully?