Ipod shuffle (4th gen) won't charge?

Does the light on the shuffle come on in any way when connected? You say it does not charge, but does the shuffle still appear in iTunes when connected? Can you still sync songs to it?

Double check the connection to the headphones jack, to make sure the plug is fully inserted into the headphones jack as seen in this document

http://support.apple.com/kb/TS3572

Other than that, since the light does not come on at all, there is no power going to the shuffle. The possible causes are (1) problem with USB port not working or not providing sufficient power, (2) faulty USB cable, or (3) problem on the shuffle, such as a bad headphones jack or logic board.

For (1), try it connected to a direct USB port on the computer (not a hub) with other USB devices disconnected. If it does not work that way, connect something else to the same port to confirm it is working, preferably something similar like a USB flash drive or bus-powered external drive.

For (2), you said you know the USB cable works, but the only way to confirm it works is to use it to connect another shuffle, or to get another cable to try with your shuffle. If you have an Apple Store nearby, you can make a reservation at the Genius Bar, and have the Apple tech give it a try with their cable.

If you have ruled out (1) and (2), it is more likely to be (3).