This fixed my problem using java 7 where I was getting the message: "Your security settings have blocked a self-signed application from running" and the game would not start.
Following the "workaround" section (see link that follows) from java's site fixed the problem. Here is the link: https://www.java.com/en/download/help/java_blocked.xml
I added http://www.havenandhearth.com and http://www.havenandhearth.com/portal/ and any other URLs that came up when I tried to start H&H to the exception list in java and that fixed the problem. I can now play using java 7. Good luck!