The normal cause of tweets not rotating is multiple installations of jQuery. That's almost certainly the problem here, because jQuery gets installed twice - and the second installation overwrites the first one and all the plug-ins linked to it.
I suggest finding the plug-in or line of theme code that puts
<script src="http://code.jquery.com/jquery-1.7.1.min.js" type="text/javascript"></script>onto the page at about line 83 of your homepage HTML and removing it.