iPod touch 4th gen dead
Error 1600 would appear to be a USB connectivity error
From Get help with iOS update and restore errors


  Check your USB connections
  
  Errors: 13, 14, 1600, 1601, 1602, 1603, 1604, 1611, 1643-1650, 2000,
  2001, 2002, 2005, 2006, 2009, 4005, 4013, 4014. You might also see a
  message that includes "invalid response."
  
  If the USB connection between your device and computer is interrupted,
  you might not be able to update or restore.
  
  To narrow down the issue, try different equipment:
  
  
  Use the USB cable that came with your device, or a different Apple USB cable. 
  Plug your cable into a different USB port directly on your computer. Don't plug it into your keyboard.
  Try a different computer.
  Solve other issues with the USB connection, then with your security software.
  
  
  If you still see the error message, check for hardware issues.


Also, you might need to troubleshoot your hardware. Try different cable, a different port, a different computer....