Q: My ipod touch wont turn on. Screen is black and doesnt reset or show a charging battery image. Have left in to charge for awhile now and nothing has changed. I got it last week.

New or used? Your info says 4th gen, which means the device is a few years old if it is indeed a 4th gen. It's possible that the battery is fritzed.

If you have an Apple Store nearby you could take it in to be evaluated.  Or if you bought it new, I would return it to the place of purchase for an exchange.

Are you plugging it into an electrical outlet to charge or using your USB cable connected to a Mac?

I had a plugin charger go bad so that it wouldn't charge my iPod, but connecting to my Mac with USB worked.

The guys at the local Apple store gave me a new plugin charger for free.

Try the remaining actions of:

https://support.apple.com/en-us/HT203435

- 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/