Setting the security level to low in the Java Control Panel should allow applets to run. Did you restart your browser after changing the security level?
If you update Java 7u51 or later, you can add an exception for the Windchill site using the new Exception Site List feature. The below Oracle blog discusses how to add a site to the ESL:
https://blogs.oracle.com/java-platform-group/entry/upcoming_exception_site_list_in