Hi there Concubar,
You may find the information in the article below helpful.
Resolve specific iTunes update and restore errors
http://support.apple.com/kb/ts3694
Check USB connections
Related errors: 13, 14, 1600-1629, 1643-1650, 2000-2009, 4000, 4005, 4013, 4014, 4016, “invalid response,” and being prompted to restore again after a restore completes.
If there’s an issue with the USB port, cable, dock, or hub, or if the device becomes disconnected during restore, try troubleshooting the USB connection, then troubleshooting your security software.
To narrow down the issue, you can also change up your hardware:
- Use another USB cable.
- Plug your cable into a different USB port on your computer.
- Try a different dock connector (or no dock).
- Add (or remove) a USB hub between your device and computer.
- Connect your computer directly to your Internet source, with no routers, hubs, or switches.
If you checked your connections and are still seeing the error message, check for hardware issues.
-Griff W.