hello, the reason internet is not working on this newly installed windows XP is becuase (most likely)you are missing network card drivers.
To verify right click "My Computer", and select "Properties", then click on "Hardware" tab and click on "Device manager" here you will see anything that is missing drivers has a yellow Excalmation mark (!).
NOw that you have checked which items are missing drivers:-
First thing you should do is open the link below on the laptop with the internet.
Download Nvidia LAN drivers on your laptop and find a way to bring it to your HP desktop, copy to flash drive, burn it on cd etc...
Install LAN drivers on your HP computer, restart your computer and test internet.
If internet is now working visit the link above again from HP computer and download all the drivers that are missing in device manager, install them one at a time.
I hope this helps. Let me know if you still have problems or get stuck at something.