The error codes are there for a reason. They provide us with information as why you aren't able to restore, for example, when security software(firewalls, virusscanners) prevent the communication between the Apple servers and the iPad, wich is needed to install new software.
I suggest taking a look at the error codes you provided and then look at this article:
Based on your information, I would recommend trying to switch off all security software and try restoring again. If this fails, on multiple computers, your iPad may need a hardware repair. Please see below for two of the codes you provided (from the article above)
These errors typically occur when security software interferes with the restore and update process. Follow Troubleshooting security software issues to resolve this issue. In rare cases, these errors may be a hardware issue. If the errors persist on another computer, the device may need service.
Also, check your hosts file to verify that it's not blocking iTunes from communicating with the update server. See iTunes: Advanced iTunes Store troubleshooting—follow steps under the heading Blocked by configuration (Mac OS X / Windows) > Rebuild network information > Mac OS X > The hosts file may also be blocking the iTunes Store. If you have software used to perform unauthorized modifications to the iOS device, uninstall this software prior to editing the hosts file to prevent that software from automatically modifying the hosts file again on restart.
Error 1004, 1013, 1638, 3014, 3194: These errors may be the result of the connection to gs.apple.com being redirected or blocked. Follow these steps to resolve these errors:
- 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.
