It could be a dirty or scratched disc, the optical drive, or even some other problems. XP's setup claims files are missing when it fails to copy a file for any reason. I've got that when there were bad sectors on the hard drive.
Laptop optical drives are usually very easy to clean unless you have a slot loader. Most of the drive mechanism is normally ejected with the tray and the laser pickup lens is right there -- you should be looking right at it with the drive in ejected state. You can clean the lens
very gently with a q-tip and rubbing alcohol. Do not apply more than the minimal possible pressure to it or you will damage the mechanism.
I'd also make a copy of your XP CD and try that. Usually one would expect a marginal drive to have even more trouble with CD-R media, but I have been pleasantly surprised before. Sometimes they just seem to like something different.
Finally (or first thing, if you prefer to just do it that way rather than keep messing around), you can install from a USB thumb drive. Use
WinToFlash or follow one of the numerous
tutorials to prep your USB drive.
