My IPod Touch, 6th generation will not charge or start. The battery symbol appears but appears to indicate battery is drained (red line at bottom).

If the battery is very low it will need to be on charge for a few minutes (I'm not sure how long - perhaps 30 minutes) before it shows any response.

Are you sure that your charger and cable are working? A clue is that if you plug the cable (with the charger plugged into the wall supply of course) into the iPod and then the red battery light comes on, that suggests that the iPod is seeing power coming in. Leave it for a while to see if the iPod eventually responds. But if the red battery indication only comes on when you try turning the iPod on, despite having power plugged into the iPod, that suggests that the cable or charger is not working.