Got it working (took way too long to figure out).
1) On to your Apple system with the Airport connection. Go to System Preferences --> Network. Select 'Show' --> Network Port Configurations. Move the order around so that the Airport is listed first, followed by the Ethernet ports.
2) Next, click the "Airport" tab and look at the settings for IP Address, Subnet Mask, and Router. You must enter this exact same information into your Ethernet settings (for each Ethernet card listed in the "Show" combo box.
3) Go to System Preferences --> Sharing. Click the Internet tab. Turn on Sharing. The description there should make perfect sense for what you want to do.
4) Now click the "Firewall" tab. Turn OFF the firewall (I tried all different combinations and the only way I could get mine to work was with the firewall OFF).
5) This step may be optional. On the "Services" tab I have "Personal File Sharing", "Remote Apple Events" and "Printer Sharing" all turned on.
6) Plug in your Ethernet cable between the Airport machine and the other system.
7) Go to the other machine and open System Preferences --> Network. Select 'Show' Built-in Ethernet. Set it to Configure for "Using DHCP".
Click Apply.
That's it....you should be on-line with both machines. Hope this helps someone else save a few frustrating hours.
