Is there a free program that will allow me to repair/recover corrupted files in Windows XP?

Start
run
chkdsk /r

Restore a restore point when you know the files were there and clean

Its hard to say if you are able to recover the file or not. It depends if you been working on the drive on which the files were deleted or disappeared from. The more work you do the drive and folder in question the probability that your files are recoverable are slim.
Search in google "Search&Recover"
From my experience you will not get to recover your files the program finds unless you buy it and then it depends how long its been since you lost them. Data gets written over all the time causing the recovery phase hard and possibly impossible.

Did you do a back up in the past?

I started getting a lot of files being corrupted about 2 weeks ago. Sometimes the file will show as corrupted, and then come back on it's own. I've been having major problems with this computer.

[url]http://www.pcinspector.de/file_recovery/UK/welcome.htm[/url] recovers files.

Try running a sfc /scannow [url]http://www.updatexp.com/scannow-sfc.html[/url]