I found an interesting article through Digg today that I decided to include here should I ever come across a similar problem.
First off,
here's the article. In summation, the problem lies with the seven DLL files that downloaded in a silent and undocumented Windows XP update two weeks ago. These DLL's sabotage update functionality after a user "Repair"s their up-to-date install of XP (using an authentic XP CD).
What happens is that those 7 DLL files are not registered with Windows; any attempts to install the 80 most recent Windows XP updates will result in failure with a cryptic, "A problem on your computer is preventing the updates from being downloaded or installed". The solution, thankfully, is quite easy:
Quoted from Windows Secrets:
Step 1. Open Notepad (or any text editor).
Step 2. Copy and paste the following command lines into the Notepad window (the /s switch runs the commands silently, freeing you from having to press Enter after each line):
regsvr32 /s wuapi.dll
regsvr32 /s wuaueng1.dll
regsvr32 /s wuaueng.dll
regsvr32 /s wucltui.dll
regsvr32 /s wups2.dll
regsvr32 /s wups.dll
regsvr32 /s wuweb.dll
Step 3. Save the file to your desktop, using a .bat or .cmd extension.
Step 4. Double-click the icon of the .bat or .cmd file.
Step 5. A command window will open, run the commands, and then close.
That's it! I've not been able to test whether that works or not, but according to the article it will indeed fix any Windows Update-related problems that may crop up.