If you have never done it before, fitting a motherboard into a case can be very difficult. If fitted incorrectly you can cause a short circut, flex the board and crack it... You do have the advantage that the cases and boards are identical so the brass pillars in the case will align with the screw holes in the motherboard and the plastic standoff pillars on the boards will be in the right place. Even so, I would err on the side of caution and move all of the components from the dead PC to the living one, leaving the motherboards where they are.
XP will be fine, the boards are identical so it shouldn't give a peep. Even if they were not, XP would just declare that it had found new hardware and search for/install new drivers.
Do wear an antistatic wrist strap when you move stuff, especially the ram. If you don't have one, any old length of electrical cable/speaker wire will do (strip one end and wrap it round your wrist, strip the other and wrap it around bare copperwork like a radiator or water pipe).