whatismyip.com:: This is your external IP address. It is the external IP address of your router. You do not need this address unless you want to play DirectIP games, where you tell your friend "Hey -- Connect to my game at (whatismyip.com)". You do not need this IP address otherwise.
IPConfig:: Your IPv4 address is your computers IP address. Your Gateway address is the routers internal IP address. Within your router configuration you would setup port forwarding to the IPv4 address that is listed in your ipconfig.
Here is a wonderful website that will give you step-by-step instructions on how to setup port forwarding for your specific router. You will need the make and model
http://portforward.com/english/routers/port_forwarding/routerindex.htm
These are the ports you will need to configure:
http://forums.civfanatics.com/showthread.php?t=146735
* 2033 (Civ4)
* 2056 (Civ4)
* 47624 (Directplay)
* 3783 (Voice Chat Port)
* 27900 (Master Server UDP Heartbeat)
* 28900 (Master Server List Request)
* 29900 (GP Connection Manager)
* 29901 (GP Search Manager)
* 13139 (Custom UDP Pings)
* 6500 (Query Port)
* 6515 (Dplay UDP)
* 2300-2400 (DirectPlay - UDP)
The best way to test if the above has worked is to go into the MP Lobby and join a game. If you have problems then I would look into disabling your other adapters. It looks like you have perhaps a VPN setup (tunnel connections) that could cause problems. You may also want to look into VISTA's security settings to allow the civilization application to open ports.
If you continue to have problems then I think you need someone to help you figure this out. Perhaps you have a networking friend that could setup ethereal, or even netcat to validate your router ip forwarding rules, and to move onto a different reason why you are unable to play via internet.