To resolve any problems with the VNC console and java, follow these steps:
Download and install the latest java here: https://java.com/en/download/
Once reinstalled, completely close your browser, reopen and then visit this page which should prompt you to activate Java: http://java.com/en/download/installed.jsp
Once activated, open the java control panel.
On Windows computers this is located in Control Panel->Programs->Java
On Mac computers this is located in System Preferences -> Java
With the java control panel open go to Security->Edit Site List-> Add->Add the following sites:
Save those changes, then close out of the browser, restart it and the VNC console applet should work now.