Why is my iPod not responding to charge?

In this case, the first thing I'd check is the condition of the pins in the dock/charge port at the bottom of the unit. Look for dust or other obstructions that may be keeping the pins from making good contact. Also, check for missing pins. You'll need good light and a magnifying glass if your eyes are like mine. :)

If the unit isn't event taking a charge, regardless of source, the first thing to do is check for quality connection. Thereafter, you might need to open the unit up to check the internal connections between the docking port and the system board.