Do you have an active internet connection on either of these computers?
If you just have the two computers connected to each other then is one of the computers giving out IP addresses?
I know that I'm asking irrelevent questions.....but, to answer your question, your network connection is disabled. Sounds like someone is playing with you

Open up your network connections in the control panel and reenable it by right-clicking on the appropriate connection and then clicking "Enable".
With newer NICs, you'll find that you will still receive an active or link light between two connections even when one of the connections is disabled. It's just trying to point out that the physical link is good
But, by default, if your connection is "Availbale" but just "Disabled" then it will shoot back a "Windows IP Configuration" with no address.....not even a 0.0.0.0, because logically, that's impossible. Ok, I'm rambling now.
In short, Re-enable your network connection
