The Windows XP SP3 disc lacks the latest version of Windows Update Agent which Windows Update and Microsoft Update requires yet, fails to download and install.  The Windows Update Agent update for Windows XP 32-bit on Microsoft's website is an out-of-date version.
If you're trying to update a fresh install of Windows XP SP3, verified the date/time on the computer is correct, and Windows Update and Microsoft Update give error messages, try installing this Windows Update Agent update and attempt to update again.  Windows Update and Microsoft Update should work. It really is as simple as: Windows Update doesn't work on XP 32-bit -> try installing this.