OK, here is where I am. After talking with the guy who manages my server, I followed the instructions from the attached link to do what Sunrise is asking.
http://dnet.net/techSupport/smtpAuthOE.asp
In this example they have entered the same server for both incoming and outgoing (not my case).
In the section 5, I put my Sunrise info. since in section 4 I am using the Sunrise SMTP server. Still no luck on it working. Sunrise is still blocking the outgoing email.
I have read the web link to the Sunrise page (above) which seems to suggest that it is still possible to use the Sunrise server to send emails.
Would someone be able to look what they have entered in their computer? I am looking for someone who is using their own server for incoming email (like me) and using Sunrise for the outgoing email. What do you have in the entered in section 5?
Many thanks.