I also have this problem. I've even attempted to apply a work around suggested on java help website but it didn't help. :(
Java Applet not loading because of 'security settings' how do I fix this?

If you're at an institution (university) you may be restricted by Group Policy settings set by the network administrator. If so, there's no way to work around them except taking the computer off the network (which would not allow you to play online anyway).

Yes I second that. If you're on a corporate or university computer system then you are kind of restricted on what you can do.
I'm at my university and I assume that is why I can't run the java applets since it seems to be because of a security reason. Live chess works fine, its just trying to play against a computer that the applet doesn't run. I've tried reinstalling java and looking through my security settings, set chess.com as a trusted site and everything else I could think of but I'm not sure where to go from here.