Thatcher - January 30, 2013 at 8:55am
Install the latest version of iTunes.
Check security software. Ensure that communication to gs.apple.com is allowed. Follow this article for assistance with security software. iTunes for Windows: Troubleshooting security software issues.
Check the hosts file. The restore will fail if there is an active entry to redirect gs.apple.com. Follow iTunes: Advanced iTunes Store troubleshooting to edit the hosts file or revert to a default hosts file. See section "Blocked by configuration: (Mac OS X/Windows) > Rebuild network information".
Try to restore from another known-good computer and network.
If the errors persist on another computer, the device may need service.
Also download/open Tiny Umbrella and make sure the 'Set hosts file on exit' is not ticked in the advanced options.