Trying to restore iPod, iTunes does not recognize it

Question

My brother's iPod suddenly became unable to charge this morning, so we decided to try and restore it as that was a common solution to this problem. Well, whenever we plug the iPod into my Mac, it shows the charging screen, then turns on shortly after with nothing charged. I went into recovery mode with much difficulty, since the iPod would turn on by itself after it was plugging and showed the charging screen, and I have gotten the screen that tells me to plug it into iTunes.
I plugged the iPod in, and iTunes won't recognize it. I tried restarting my Mac, using a different cable and a different port, tried plugging it into the ports on our PC: nothing. The screen keeps telling us to plug it in, but obviously this isn't working.
We've tried both recovery mode and dfu mode and now I'm at a loss at what to do. Help please?

Answer 1

Not Charge
- See:    
iPod touch: Hardware troubleshooting
iPhone and iPod touch: Charging the battery
- Try another cable. The cable for 5G iPod (lightning connector) seems to be more prone to failure than the older cable.
- If a 5G iPod
Iphone 5 lightning port charging problem - SOLUTION!
- Try another charging source
- Inspect the dock connector on the iPod for bent or missing contacts, foreign material, corroded contacts, broken, missing or cracked plastic.
and
Try:                                               
- iOS: Not responding or does not turn on
- Also try DFU mode after try recovery mode
How to put iPod touch / iPhone into DFU mode « Karthik's scribblings
- 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.
  Apple Retail Store - Genius Bar