First have a look inside the dock connector and check for any dirt or other objects and clean them out if there is any
Second I would recommend leaving the iPad mini on a AC wall charger for a few hours and then have another look to see if the iPad is working
Failing all that, its time to send your iPad back to Apple as it will still be covered by the warranty and since you have not damaged it, you will not want to pay out for any repairs
Let me know how you get on and which method leads to success, if you need any more help please ask
Cheers
Brendan Mills