Today I updated my Java version to 7u51. After the installation, I cleared Java Cache, browser\'s Cache, and logged into a secure website that uses an Applet to provide cert
We had the same problems with IE11 and new Java. Try to add your site to compatibility view. You can find here how to do it.
How to enable compatibility view in Internet Explorer 11
You can try now if it works or not. After that you can remove site from compatibility view and it should also run.