I always recommend isolating the problem as quickly as possible. First figure out if the modem and router are working properly. Connect with any other device to the internet to check this. If other devices can connect than this is an issue with your computer, in which case the guide Matthew suggested is perfect.
Yeah, $12.00 seems a bit expensive. You can pick them up at Shenzhen Parts for $3.00, but there is shipping costs from China. http://shenzhenparts.com/iphone-5c-lcd-shield-plate.html
Most likely the dock connector flex is blown. It is really difficult locating parts for the Shuffle though, so most likely you won't be able to save. Love the MacGyver charger though!
