Hi cliu,
Please refer to http://www.cutesoft.net/live-support/Developer-Guide/scr/Adding-chat-button-tag.htm, check the deploy code
<script src="http://www.cutesoft.net/CuteSoft_Client/CuteChat/Support-Image-Button.js.aspx"></script>
<script src="http://www.cutesoft.net/CuteSoft_Client/CuteChat/Support-Visitor-monitor.js.aspx"></script>
CuteLiveSupport has not a page name "Support-Image-Button-QMIHome.js.aspx ", that is why the button does not show up. I thought this is your old chat button page created by your developer?
<script src='http://support.roll-a-way.com/CuteSoft_Client/CuteChat/Support-Image-Button-QMIHome.js.aspx'>
Regards,
Ken