It may actually be your cord. You can use a standard non-polarized plug to test your Nano, such as one in a dvd player, gaming console, electric shaver, etc..
If the light comes on it indicates your E-Nano plug is faulty and you will need a replacement. You will need to fill out an RMA REQUEST to request a new cord. You will not need to send back in your unit nor will you need to pay for the replacement if you cord is still under warranty.
If your led light is still not functioning, you will want to send in your unit for additional testing.