Hi
Sorry I'm kind of late getting back here, I didn't get a notice that you had posted.
I'm guessing you have gotten this solved by now but this is how to factory reset a Gateway laptop.
1. Reboot, and press F11 or the R key to start the recovery process (keep tapping the key from the start of boot up).
2. Select either "Full System Restore (Destructive ***This will erase all your unsaved data!***)" or "Full System Restore (With Backup)"*.
3. Click "Next", and then click "Yes" to confirm the recovery process.
4.Wait for the computer to restore itself.
When it is done, click "Reboot" to reboot the computer.
I have to say these are the clearest instructions I found and there were others that gave different ways of starting the process.
I couldn't find this info on the Gateway website all my searches came back to "How to reset my Android tablet".
Mike