The Backup program is installed automatically on XP Professional, but not on XP Home. If you have the genuine bootable XP Home installation CD, insert it into your system and browse to this folder:
\ValueAdd\MSFT\NTBACKUP
Double click the ntbackup.msi file to begin the installation.
Here is a nice Microsoft article that tells you all about it:
http://support.microsoft.com/?kbid=302894
Here is another article that tells you how to do it:
http://www.winxptutor.com/ntbackup.htm
If you don't have an installation CD and need to download the ntbackup.msi file, here is the link so you can download it:
http://www.winxptutor.com/ntbackup.htm
How often do you perform such an operation?
I have been running this installation for close to 9 years and never done a Repair, Reinstall or used System Restore to fix any problem (but I have practiced so I know how the work - and don't).
If you have a genuine bootable XP installation CD that is not SP3, would you like to learn how to use that to create a new XP installation CD that has all your drivers and SP3 already on it? At least that will save you some time if you decide to reinstall from scratch. It will not help you with your third part applications though.
Here is one such article to get you started:
http://www.bleepingcomputer.com/tutorials/slipstreaming-windows-xp-to-create-bootable-cd/