You said you did all in the list in apple web suggestion, so what did Apple say when you contacted them about your issue?  That is the last part of the troubleshooting steps outlined here:

If you see error 9, 4005, 4013, or 4014 when you restore your iOS device

When you try to update or restore your iPhone, iPad, or iPod touch, you might see one of these messages in iTunes.

If your iOS device disconnects during the update or restore or if iTunes couldn't tell the device to restore, you might see one of these messages:

• The iPhone [device name] could not be restored. An unknown error occurred (9).
• The iPhone [device name] could not be restored. An unknown error occurred (4005).
• The iPhone [device name] could not be restored. An unknown error occurred (4013).
• The iPhone [device name] could not be restored. An unknown error occurred (4014).

Try these steps to restore your iOS device:

1. Install the latest version of iTunes.
2. Restart your computer.
3. Check for updates to your Mac or PC. If you restart your computer for an update, check for updates again after you restart.
4. Try to restore your device using another USB cable.
5. Try to restore your device on another computer.
6. Force your device to restart.

If you continue to see error 4005, 4013, or 4014 when you try to restore your iPhone, iPad, or iPod touch, contact us.

Learn more about other update and restore errors.