Thank you for the uploaded picture. That makes things easier on our end!
Based on my experience with iPod Touch 4's, it seems that the LCD is gone. This can be repaired by replacing the LCD/Digitizer unit (they are glued together and therefore, need to replaced together). Use this guide. You can buy the needed part here.
The only thing you have to do after you got the new part and before finally installing it: Transfer the metal holder (top) and the home button (buttom) of the old display assembly onto the new one. Also, by some new adhesive for the bezel and home button area and put it on the old plastic bezel and home button area.