Have you tried the Last known Good configuration option?
Try running ChkDsk /r from the Recovery Console.
HOW TO: Install and Use the Recovery Console for Windows XP (Q307654)
You could also look at a recovery console procedure when unable to start computer due to corrupt registry.
This is a layman's version of Q307545 in simple language.
If they don't work you could try repairing windows by running it over itself. You will lose all your windows updates (no problem if you substitute them with SP2) but your files and programs will be untouched.
How to Perform an In-Place Upgrade (Reinstallation) of Windows XP (Q315341)
Trying to save files to DVD from a failing operating system requires some means of running the burning software in the first place. If the above don't help you might want to consider a parallel install of XP.
266465 - HOW TO: Perform a Parallel Installation of Windows 2000
You can do the same with XP. Don't install any unnecessary programs, just keep the parallel installation as simple as possible.
Or the paragraph in this article.
"To install Windows XP to a new folder (to perform a parallel installation):"
How to install or upgrade to Windows XP
Another consideration would be something like this - BartPE which is a mini XP running on just CD but able to access the hard drives. This is more useful in saving data to just a second partition however, although some CD burning may be possible.