Since you can't connect with the new computer, we must assume that there is indeed a difference in the setup, either of LW and/or of your system.
Did you install LW while being logged in as administrator?
Then, did you open the listening port number in your firewall as shown under LW>Tools>Options>Advanced>Firewall Configuration ?
Did you open said port in your firewall as TCP and UDP?
Do you see a small brickwall in front of the globe in the bottom left corner of LW?
