Static builds up on your body and the "charge" is transferred to anything you touch - at the point of touching and at the moment of touching. If the charge on your body is above 5000 volts you may feel it as it jumps - particularly noticeable in the winter.
A static discharge can destroy a tiny connection in delicate electronic components.
It may well have been a static discharge that harmed the MP3 player - it's unlikely that the device could give you a shock on its own - you probably gave it a shock.
Take some comfort that without an MP3 player your child may feel deprived but will not be harmed - kids can cope with stuff like this and her hurt will not be remembered into adulthood. Read her a story instead - she'll remember that all he life.
Good luck...
Peccavi
March 2010