Problems receiving mails

[wabbz111]

I am new to Zimbra and i have installed it on my local(LAN) mail server. My ISP provided me with a public IP address which is natted to the LAN ip address of the mail server. This was done to allow me to send mails to external mail servers( i.e Gmail, Yahoomail etc).
I can send and receive emails within my network.I can also receive mails from external mail servers(i.e Gmail, Yahoomail etc)
The challenge iam having is that whilst i can send mails to external mail servers (i.e Gmail, Yahoomail etc) and receive a confirmation from Zimbra that the mail has been sent, the mails never reach the inboxes of these external servers.
Furthermore i do not receive an error that the mail bounced or delivery failed.
For testing purposes i tried to send from Zimbra to a non existent Gmail address and that promptly showed a failed delivery with the error of non-existent email address.
It seems that Zimbra is sending the emails to their destinations and checking if they are valid but they are just not reaching the inbox of Gmail, YahooMail or any other external mail server.