I highly recommend to not use any third party websites for iTunes in your case, as they are not certified or approved for use by Apple. Also, I recommend following the below steps to see if it can isolate & fix the problem:
- Place the iPod in DFU (Device Firmware Upgrade) mode and then restore. In order to do so, follow the below steps:
Step 1: Turn off your iPod and connect to PC / mac
Step 2: Hold down the Power button for 3 seconds
Step 3: Without releasing the power button, also hold the Home button for 10 seconds
Step 4: Without releasing the home button, release the power button and keep holding the Home button for 20 seconds.
- Try on another computer
- Try another cable
- Also, confirm your security software and settings are allowing communication between your device and update servers.
In your situation, I also recommend to go to your local Genius Bar Reservation and/or contact Apple Support directly as they have more options to better assist this matter if the above solutions don't fix the issue.