When u put a URL into a browser it searches for a DNS Server to find that name and subsequent IP. Make sure you are not running any DNS Server on your LAN which I doubt u are - then make sure the comp the Webserver is running on has a STATIC IP along with at least 2 DNS Server URL's/IP's designated. Usually your ROUTER will show which DNS Url's you are using. Take those and specifically set the comp DNS to those url's.

Then try to punch in your internet addr. on the webserver.