If you have the client side developer window up, you can see some of the calls that are happening and possibly errors.
Most likely you are running into Cross Reference/Click Jack blocking.
I believe this is something you can disable at your own risk within Tomcat, not sure if Windchill has a setting for it.
A colleague helped me on this topic and I successfully displayed Windhcill in a Mashup !
Here after is the solution.
Try to add this to %WT_HOME%/codebase/WEB-INF/web.xml
<description>Filter to monitor servlet requests as a whole; should always be first in filter list</description>
<!-- Initialization parameters for ServletRequestMonitor; must be writable JMX attributes of ServletRequestMonitorMBean -->
<!-- Note: these settings will normally be overwritten by MBeanLoader injection after initial MBeanLoader save -->
In Yellow is the text to add.