iPod stuck in DFU mode and iTunes keeps prompting to put in DFU mode

Older ipod touch is stuck in dfu mode -- indicates to plug into usb port and open itunes.

I tunes indicates the ipod must be restore. Select the restore button.

An error dialog pops up telling me it was once in dfu mode but was restarted and that I need to disconnect from the pc and place it in dfu mode.

Attempt several different methods to do so but with no avail. Itunes continues to repeat the message.

Endless loop. If the thing if dead, please just tell me.

Same result on multiple PCs.

[Re-Titled by Moderator]