Hi PA
Had you noticed the battery life getting really short before it stopped working? If you've used it a lot, the battery may not be able to take a charge any more. There's some info on Apple's website about repair centres and sending it away for a new battery and so on.
You might want to look on there for the info on resetting it too - mine is a nano and with that you hold the central button and top part of the touch wheel in for 8-10 seconds ( you may have to do it several times). I don't know if it's the same for a shuffle.
Hope you get it working soon :)
Jennie
January 2009