Until an expert comes along with the definitive answer here's what I understood.
It doesn't matter which copy of XP you use for reinstallation (you can borrow one if you like) as long as your hardware profile matches with your authentication key then everything is ok. As you have already used the key previously they would have recorded your hardware profile (mobo,hdd etc.).
Now I'm waiting for someone to come along and shoot me down in flames, metaphorically speaking of course, it is a pilot's forum after all.