Your reply doesn't really tell us how you have things set.
"New Ticket:" and "New Ticket by Staff:" should probably be enabled.
("New Ticket by Staff" is optional really depending on how you have tickets opened. Where I work we do not open tickets for other people, so we have it disabled.)
What do you have "Outgoing Emails:" set to? If the above is set correctly and you have this set to "None: Use PHP mail function" You might try going to the email tab and setting up SMTP Authentication under the email in the Emails tab.
What OS / Webserver / Mail server are you running?
