I have had this issue come up multiple times when playing at home or bringing my laptop to my friends house and it can get quite annoying. I have solved the issue for myself, I hope this helps the rest of you that run into this. Note I am using Windows XP.
1. First of all their needs to be some setting changes in the game if you are using multiple computers on a network at home.
–A. Start up the Warcraft CD and click on Options, and then click on Gameplay.
–B. You will see a game port number listed here. Typically the first number is 6112. For every machine on your system increment this number with 6112 being your first computer and 6113 for your next and so on. Once you have made the port number change keep note of which computer has what port. Close Warcraft when finished.
2. Now we need to make some firewall changes in your router (if you have router). I use a Linksys router and I will show you what must be changed. To get to your router you must open up a browser and type the appropriate IP address. Typically routers are http://192.168.1.1 If this does not work for you - you will have to consult your router’s manual.
–A. A username and password will be asked for. If you have a Linksys router the typical username can be anything and the password is admin. If this does not work consult the manual again.
–B. Navigate to the Port Forwarding section of your router options. For my Linksys I will be clicking on Advanced and then clicking on Forwarding. Enter the port number for each computer from step 1 and the associated IP address for that computer.
–C. To get your computers IP address click on the windows Start menu and then click on Run. In the run window type cmd and hit enter. Now in the black box that pops up type ipconfig and hit enter. This will tell you this computers IP address.
–D. As you can see below I have port 6112 associated with IP address 192.168.1.110 and port 6113 associated with IP address 192.168.1.111. Once you have this all filled out accordingly save the changed settings to your router and then close the router window.

3. Now we must fix a problem with Windows firewall that Windows XP service pack 2 caused us. This is an easy fix and you do NOT want to uninstall service pack 2 nor do you want to disable the windows firewall.
–A. Click on the Start menu and then click on Control Panel.
–B. Double click on Network Connections.
–C. Right click on Local Area Connection and go to properties.
–D. Click on the advanced tab.
–E. In the windows firewall box click on Settings.
–F. In the windows firewall window click on the Exceptions tab.
–G. You may already see some warcraft exceptions in here but chances are they are pointing to an incorrect file to make the game play properly. So we will add it to make sure. Click on Add Program.
–H. Navigate to the Warcraft III folder and locate War3.exe. My path is C:\Program Files\Warcraft III\War3.exe. With the War3.exe file highlighted click on OK to add it to the list of exceptions. You should see War3 in the list now. Close the windows.
You should be able to fire up Warcraft and create a game without problems of people joining now on any computer in your network. This solved all of my problems when I figured this out. I hope it helps you as well.
(Note that I have set up static IP’s on all of my computers so that the IP address does not change. If the IP address changes you will have the same problem and need to just adjust the IP addresses in your router’s firewall accordingly.)