Does the other laptop have a recovery partition? If so, you could copy that to yours and see if it's able to reinstall the OS.
Of course, you'd then need to install about 15,000,000 Windows updates to get to the latest version of XP.
Copying the drivers should be possible if you can find the relevant .ini and driver files, but would take some trial and error to figure out which ones you need. Unless you get lucky, and the manufacturer put them in an easily-found driver install directory.