Sorry forgot to add you can use your working computer to dowload the sevice pack and then place it on a cd and load it on the other, But you have to get it from a third party, NOT microsoft, they do allow you to save SP2 to your hard drive, try
www.downloads.com or just google "windows xp sp2" if your copy of windows only has service pack one on it its always a good idea to have SP2 on a disk somewhere, however service packs wont be the difference in getting online or not, but I do-not suggest going online without SP2 unless you enjoy deleting files from safe mode