You should check that you have the latest version of Moodle 2.0.2+ and if not request that they update it for you.
There was an issue in earlier versions of Moodle 2 where Moodle called https instead of http on occasions. This happened only on Zeus (and perhaps Litespeed) servers. So using https and an SSL cert should be your choice and not essential for Moodle to work. Don't know if you had the above problem but if so this may help.