You're not the only one who is confused.
If your PC is in the same state now before the install of XP as it was when you installed XP the first time, and you use the same CD and the same licence key, it should work. So something must be different. But it's not clear from your story what is different.
If you came as far with installing to have XP asking for the product key, most likely the old one is already gone from the hard disk. It's only in Windows 8 that it starts asking for the key in stead of ending with it.
And just for interest: what OS did this laptop come with originally?