Ben,
I ran into the same problem after those updates were installed. We are running IE9, JRE7u51, Windchill 10.1 M030. I found that after the installation of the patches, IE wants the JRE updated. Our IT department is working on a fix, but if you close all browsers and delete everything below the folder C:\Users\<userid>\AppData\Local\Microsoft\Internet Explorer and restart IE, it all works again, with the patches installed.
Mike Ibosh