A quick comment to eliminate the chance that you may be doing this .... Moodle does not support frontend / backend logins like joomla does. Therefore if you are logging into moodle as both user and admin or user and teacher, you will need to use multiple browsers (ie chrome, ie, ff, etc.) otherwise sessions will get confused. For example login as student using, say chrome, through joomla. Using FF or IE log into Moodle directly for teacher or admin.
That said, as Antonio mentioned the error msgs you are getting are unique and do not suggest the above scenario but worth eliminating the issue just in case.
