Hi Wired4fx, welcome to the forums.
You mention that your system uses DNS through a DSL modem. Is your server behind a NAT? If so, you'll need an internal DNS server or separate view on your DNS server so your server can resolve itself to its internal IP address as well as the MX for your domain. Zimbra is very dependent upon DNS, especially the MTA (postfix) and LDAP. Here's the Zimbra wiki article on using a "split DNS" setup using Red Hat:
Split DNS - Zimbra :: Wiki Of course it's slightly different in Ubuntu, but the concept will be the same.