you will have to open up your windows firewall and know your IP address to get it working.
There is a text file in your NR2003 folder that will explain what you need to do. It requires port forwarding as well... it's not too hard, but a bit difficult to get your head around... It's been so long since I did it, I couldn't even tell you how off the top of my head.
A much easier solution might be for both of you to download the NRT Servers free lobby software that lets you both race on the free NRT server online. Your limited to the tracks they have racing at the time, but at least you can race your buddy and see how good you guys are.