Try that recovery disc in a friend’s PC to see if it can read and make a copy of it. If so, then your laptop most likely has a failing CD drive or it needs cleaning.
As the first recovery disc is most likely the OS only, you can try getting a copy of the Windows XP Home CD from someone else and use the Windows product key printed on the bottom of your laptop during installation.
I would strongly recommend avoiding purchasing XP Home from an unofficial source (e.g. eBay), as even if you use own XP product key during installation, there is always the risk that the unofficial CD may have malware, patches (to circumvent activation), etc. that could potentially lead to activation problems later on after a WGA Windows updade or even resulting in your own XP key being blacklisted.
Once you get the OS disc, boot it and go into the Recovery console. At the prompt, type in “chkdsk /f C:” to run a check on the OS drive. In over half the BSOD’s on boot I’ve seen, these were fixed by simply running chkdsk on the drive.