Actually, this doesn't work.. You can't take any product key and make it work with any disc(as far as XP is concerned)..
For instance, you can't take a Sony OEM OS disc (which was usually a set of restore discs before they started using restore partitions instead) and
install it on another system using a different product key.. Or you can't take an XP SP1 disc and use a product key from an XP SP2 disc(or the product key on the machine)..
Or you can't take a Home key and use it with a Professional disc..
I'm sorry if I simplified things too much. Of course different versions of XP (Home, Pro, Corporate) have different series of license codes. Even OEM and retail codes don't mix. Plus there's some manufacturer versions, that don't allow installing from any other source than theirs. AFAIK you can use a standard unbranded OEM XP Home CD with an HP or Fujitsu-Siemens code, also with some local minor brands and activate them quite effortlessly.
And yes, SPKmes, if you tell MS that the license code is used on more than one machine, they have all good reasons to hang up. One license is for one machine only, unless we are talking about volume licenses, which don't need activating at all. But that's another story.
So if you bought this machine for your little girl with a functional windows installed into it, and the activation was left to be done by you, then you either are the sole owner of that license and thus it's used on only one machine and should be able to be activated with no problems, OR you have been cheated when you bought the machine, in which case you have the possibility to get a legal license for free by revealing the vendor to MS.
So the first thing is to find out the license code used in the installation, second make sure it's been used in your machine only, and third, if it's yours only, activate it. Otherwise, the only legal things to get your Windows working are either to buy a license or to reveal the vendor. Read here about
MS genuine software.
Or get a Linux, that's legal too. Ubuntu is actually very nice and intuitive.
And if you really need to reinstall XP from a CD, make sure your machine boots from the CD as a first option. The rest should only need reading skills. If you need additional help doing it, google for it like
this.