The Apple Mac operating system provides an interesting feature that allows you to share your Mac internet connection via the AirPort. For example, you can have your Mac Mini or other Mac computer hooked up to your DSL or Cable Modem via the cable connection, and then share that connection via the wireless AirPort as a wireless router. Then any computer with a wireless connection can access the internet just as if you had a stand alone wireless router. This saves the need to purchase a wireless router, or wireless access point and router combination. There is one major hurdle however if you try to access the wireless network using a windows system.
The internet sharing feature of the Mac OS was very impressive, that is until you try to connect a Windows machine to the wireless shared internet connection. If you do not enable WEP security on the Mac shared AirPort connection, then you are good to go. Everything works perfectly to connect your Windows machine to the wireless network. This is not ideal however, since anyone within the wireless network range can then use your network and steel bandwidth. It is highly recommended that you enable the WEP security. This is where the problem starts however. Once WEP security is enabled and you enter your password, the Windows machine can no longer connect, even though you enter the same WEP password on the Windows machine. The secret setting to getting this to work is that you have to enable the network authentication type as "shared." Depending on your wireless network hardware, there will be various software configuration tools. Browse through the settings and make sure the Network Authentication is set to "shared." Once you enable this, and enter your WEP security password, the Windows system will connect and you will be good to go.
A great article with detailed instructions on how to configure your Mac internet share and enable your Windows PC to connect ca be found at "How to connect windows computer to Mac wireless internet share".
Hopefully this has saved you considerable time and frustration.