I assume you want people outside your network to be able to see your web site?
If so, first thing you must make sure if that your ISP allows inbound port 80 traffic.
Second thing is you will have to portmap your router (and port 80) to your web server.
If you're going to 192.168.1.1 (or something similar) then yes, your router will come up, but if you're going to the IP shown at
http://www.WhatIsMyIP.com then you shouldn't see your router setup.
Another thing to be aware of is your ISP probably doesn't give you a static IP, so that address is going to change often (daily even).
You can get a service like DynDNS to update a host name (like yourname.dyndns.com) and it'll always map to your current IP (kind of like a domain, but I think it's free).
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