Well, I would personally reformat that sucker. That way everything gets whiped out. Then, reinstall Windows. Then once installation is complete Windows will prompt you to set up the Administrative account. Then it will ask for a password. Set up a password. Once all that is taken care of, and you're in Windows as you should be, go into...
Start>Setting>Control Panel (Depending on what type of theme you have Settings may or may not be there, either way you'll get to the same Place).
Once in control Panel, select User Accounts.
Once you're in user accounts, click on Create Account. Type in the Account name, then establish what powers it will have. Then after that establish a password for that account. Reboot your CPU, and try logging into that account.
If you can successfully log into that account, and you can verify that it does indeed have Administrative powers, just do this by going into Control Panel>user Accounts, and right at that screne it will tell you what users have what.
Now, depending on what you want to do, if you want to have each of your children have an account, then you can create new accounts in there. Although, I wouldn't advise giving children there own accounts, when you can save disk space just by turning the Guest account on. This will make their account safe, and you can turn it on or off, works great if you want to punish the, form the computer!
Anywho, if you do want to give them each their own account, then just click on Create Account in the User Accounts in control panel. And follow the steps.
Seeing as how each time your DPI was set to 150, and your system suggested 96, I would leave it at 96. Just to be safe.
Also, should this turn out to be a failure once again. I wouldn't call gateway, we already know how good they are! Instead, go to your local PC repair shop, tell them your problems, ask for any suggestions. If they advise you to bring the computer to them, then do so. They can help you with anything. Because the guys at the PC shop are more then likly more knowledgable then Gateway's guys.
If the tech guy discovers a problem, and he more then likly will if there is, then you can take action against Gateway, claiming that they failed to issue you a new Hard Drive, although you paid for it, and then complain that they failed to give you any reliable services.
Anywho, I hope all turns out well. If you have ANY problems, come to us, screw Gateway. The people here have a LOT of knowledge about computers. Mainly the Gurus and some other members. So get back if you need to. And make a thread at any time you want to. Chances are someone will be on to answer your question. Hope eveything turns out OK!