The reply about telnet would be the solution. You don't have access from the Zimbra machine out to another mail server. That's why it's timing out.
When an MTA sends mail it looks up the MX record out of DNS to see where it should go and then connects to the machine to send the message.
SMTP is TCP based so you should be able to use telnet to port 25 (the SMTP port) and get a connection. This when this times out it's a sign that there is no route. Normally a router or firewall config issue.
You can use the dig command to find the MX record of the reciever. |