Your internet provider is blocking you from using anyone's outgoing mail servers but their own. Many major ISP's are blocking outgoing emails. The reason they do this is to prevent you from using their internet connection for spamming purposes. You will still be able to send emails, but only by using your ISP'S outgoing mail server. Every ISP's outgoing mail address is different, but for the most part they will be mail.yourispname.com For example, if you had hosting with AOL.com, their outgoing mail server would look like this: mail.aol.com If mail.yourisp.com does not work and you are still unable to send emails, you will need to call your internet service provider to find out what their outgoing mail server is.
We also have exim running on port 26 for this very reason. A possible work around is to change your outgoing mail to port 26