I am not sure what the TW (time warner?) servers require but I do know standard ports for SMTP are as follows:
-port 25 for non ssl
-465 for SSL
-587 for TSL
If it is time warner,
here is a list of their servers based on region.
Also, pretty much every SMTP mail system REQUIRES username and password authentication which is actually optional in the setup. Make sure you have this enabled. (Should be the same as incomming server)