I just spent an hour with d-link customer support to get the answer. It wasn't clear from the installation instructions but here are the steps to get the email to work.
1) You must configure a primary and secondary DNS. Under SETUP => Network Setup, put in the primary and secondary DNS IP addresses. If you don't have one, use the generic 4.2.2.2 and 4.2.2.3.
The s/w is trying to reconcile where to send the mail by resolving the IP address. Without the DNS gateway servers, the tests will fail since it can't resolve the smtp server <-> IP address.
2) in the SETUP => SNAPSHOT webpage, put in the name of your SMTP server and all your other required information. Port 25 is the usual outgoing mail port, but sometimes you need to use 587. If the "TEST" email doesn't work, trying looking up the ip address of your service provider's smtp server.
for example, the smtp.broadband.rogers.com server's ip address is 206.190.36.18. I was able to get my emails to be sent correctly using the IP address. However, once I got the DNS servers input correctly I was able to switch back to using the smtp.broadband.rogers.com name.
hope this helps.