Thanks for that. I will check out what you said and give it a go. Thanks.

My two-month nightmare is over. After buying a Wii which worked perfectly with my router, I decided it wasn't the router but the computer. This led me to update my wireless drivers to the latest version and use the manufacturer's connection software instead of Windows XP's and it now works like it should have done in the first place.
Of course, I entirely blame Microsoft. Window XP's wireless connection software is called WZC or Wireless Zero Configuration, but perhaps Wireless Zero Information would be a more accurate name.
