Q: my newish (May 2016) ipod touch will not turn on

- iOS: Not responding or does not turn on
https://support.apple.com/en-us/HT201412
- Also try DFU mode after try recovery mode
How to put iPod touch / iPhone into DFU mode « Karthik's scribblings
https://geekindisguise.wordpress.com/2009/07/16/how-to-put-ipod-touch-iphone-int o-dfu-mode/
- If not successful and you can't fully turn the iOS device fully off, let the battery fully drain. After charging for an least an hour try the above again.
- Try another cable   
- Try on another computer   
- If still not successful that usually indicates a hardware problem and an appointment at the Genius Bar of an Apple store is in order.
how do you make a genius bar appointment? | Apple Support Communities
Apple Retail Store - Genius Bar 
https://www.apple.com/retail/geniusbar/