It would appear either way you'll need access to a working computer in order to aid your ailing one.
If your going to remove the drive & connect it to another Windows PC then you will need to determine whether the drive is SATA or IDE, which both require different interfaces. Your drive will be of the 2.5" (smaller) variety as you have stated it is a laptop.
However by far the cheapest fix (free) would be to download & burn an image of a Linux distro to disc (CD R/RW.) Try downloading Ubuntu on a working computer:
http://www.ubuntu.com/desktop/get-ubuntu/downloadThen burning the .iso image to CDR or CDRW using BurnCDCC:
http://www.snapfiles.com/get/burncdcc.htmlThen, ensuring the BIOS boot order is set to boot from your CD/DVD drive before the first hard disk, boot from your newly created CD by powering on with CD in the drive. You will then be able to browse & backup your important files to USB stick from the running Ubuntu live CD, which bypasses Windows & runs totally in the system's RAM.
However bear in mind this assumes you have a manufacturers restore disk or an original Microsoft Windows XP disc to reformat and reinstall the Operating System after rescuing your important files.
Also this is only the last resort failing all other methods.
Post back if you need any further help.