That XP disk you have won't install on the computer because you are missing the SATA drivers on it. The best way of getting this fixed is to contact Gateway and ask them to get you a restore disk for your laptop. It may cost a bit, but any other method is not easy.
If you want to get this to work, and it may not, get an XP SP3 OEM disk that will detect the SATA drive. Even then it's not guarateed to work with the code you have.