my ipod nano 4th generation won't charge

I tried plugging my Ipod Nano 4th generation into my computer to charge it (it's completely dead) and it will turn on for a second then say "low battery" and to connect to power and shut off again..and if I keep it plugged in, it'll just keep doing that over and over again until I unplug it from the computer (in which then it's just still dead). My computer won't even recognized that anythings plugged in, but I know it's not my computer because I just got done charging my kindle through the same USB port. Any ideas how to fix this?