I've never actually used it, so I can't guarantee it'll work, but I think you can set up a network bridge.
On the PC that connects to your AirPort router, open <B>Control Panel | Network Connections</B>. Select the two connections that you want to bridge (should be the computer's wired ethernet port and its wireless ethernet port) and select <B>Advanced | Bridge Connections</B>. It'll take a minute to bridge the connections, then you'll see a new item called "Network Bridge". Then, just connect your other PC to the wired port. I *think* that's all you have to do, but like I said, I've never actually tried it, so I'm not sure.
One thing, to connect the two PCs, make sure you either use a hub/switch, or get a crossover ethernet cable and connect the two machines directly. If you're actually using a router as you say, just use the "computer" ports, don't connect anything to the WAN port.
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