I had the same problem on both a W2K and WXP machine. The prob was software based, in that you have to make sure that 1) you're using a broadcasting local IP for your router - which you are because the 2nd comp works, and 2) the 1st comp is looking for the AP properly.
The problem with ensuring that you're accessing the AP properly is that there are a lot of options...WiFi is not user-friendly on Windows. I don't quite remember what I did, but I do remember that I spent a good deal of time ensuring that the driver was installed properly, that the driver was manually assigned an IP addy, etc. etc.
Good luck.
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