I prefer to keep assistance info on this site, so that others might be helped as well.

It looks like Time Warner cable does not offer static IP addresses using their residential service. You may have to upgrade to business class service to get one. What that would cost in your area, I don't know - you would have to check.

As long as you are only accessing the site using the IP address, you can still set up the port forwarding needed, you just need to remember that when your IP address changes you will have to adjust the port forwarding.

Below are some links that might help with your router:

http://forum.portforward.com/YaBB.cgi?num=1221355645
http://img412.imageshack.us/img412/4972/17937720iu1.jpg

http://www.simpleportforwarding.com/supported-routers