Technically I believe that green granite may be correct, because the Sony laptop license is for an OEM version of Windows XP.
However, reading the MS license Ts & Cs (which I have had to do from time to time), it is clear that an OEM license obtained with a pre-installed copy of XP CANNOT be used on any other PC, but it is not made clear whether or not the installation media from a genuine standalone copy may be used with the license key from an OEM copy.
Assuming that the OS license sticker on the Sony laptop is for Win XP, then my personal (not PPRuNe's) common sense view would be to try it, and if it works I think you are on reasonably firm ground, insofar as you have 2 PCs, and each PC has a license for the product installed. You would be in a lot better position than many!
I am not a lawyer, however, so please satisfy yourself that what you are doing is in accordance with the MS licensing agreement.
SD