You need:
a) name resolution working properly so *all* computers everywhere can see the server and its domains
b) server configured to use the domain name in your vhost
c) your Zen Cart configure.php files set to use the publicly-reachable domain name

http://www.zen-cart.com/forum/showthread.php?t=146848

If you're looking for help in properly setting up a homespun webserver to run websites either casually or professionally, I suggest taking that discussion to a forum which specializes on that topic, like webhostingtalk.com

The only part of your problem that's related to Zen Cart is the configure.php files needing the correct publicly-accessible domain name.