as rab777hp said, it sounds like a dead battery - they don't last forever unfortunately.
there is a teardown for the iPod shuffle 2nd generation, [http://www.ifixit.com/Teardown/iPod-Shuffle-2nd-Generation/437/1|here]
unfortunately replacing the battery requires soldering, but if you can find a replacement battery and know how to solder, it should not be difficult to do it yourself