Just to clarify - the default install is set up to use the Jobe test server, jobe2.cosc.canterbury.ac.nz. This should work with all normal question types, but it can (rarely) become overloaded. The error messages you're getting suggest that your Moodle server is not actually connecting to the Jobe server at all, except perhaps once (by luck?!) when you were trying the Java Program question type. I can't think of any situation that would consistently lead to the Java Program question type working correctly and all other question types failing. I suggest you try again and see if the symptoms are the same. If the Java Program question continues to work while other question types fail, we'll need to look more closely into the problem, but I think it's unlikely.
If all question types give you that message, then either the site administration settings are wrong for the CodeRunner plugin (check that the Jobe server and Jobe API key settings both have their default values) or your Moodle server is unable to access Jobe2 (firefall or network overload?).
Certainly, as Martin said, you will need to install your own Jobe server if you wish to make use of CodeRunner on a production server.