Although the official solution involves reinstalling the framework after manipulating the registry with the installer cleanup tool, there's a much simpler way to fix this:
1. Instead of using Windows Update, download the KB928366 package from Here
Click the Download button and save to the Desktop.
Do not install yet.
2. Download the .Net framework 1.1 redistributable package from Here
Click the Download button & save to the Desktop.
3. Download the trial version of WinRAR from Here & install it.
Right click on the dotnetfx.exe file and choose Open with ..., select WinRAR archiver.
Highlight all of the following files:
Click the Extract button & put them in a new folder like C:\Windows\Temp\DotNetFix
4. Double click the NDP1.1sp1-KB928366-X86.exe file to begin installation of the dreaded update.
It will soon complain that it can't find the installation CD-ROM (don't ask me why).
Browse to the C:\Windows\Temp\DotNetFix folder & click OK or Open
(Fix courtesy of Patrick Philippot - Microsoft MVP MainSoft Consulting Services)