I'd try running the cloned drive on the desktop it works on and sysprep it. Sysprep on XP was a bit hit and miss with the way it handled pre-installed drivers, so you may get lucky, or you may not. You may want to try uninstalling most of them on the desktop, before the sysprep. When it's shut itself down, plonk it into the laptop and turn it on. It'll then start up like it's booting for the first time, so you may get lucky and that fixes it.

Obviously you'll then need to put all of the correct drivers onto it, and activate it with a key.