We recommend taking your iPad to an Apple Store where hopefully (they mostly always do) they will replace your iPad with a new one. The price of this is normally half of what you have paid for it.
Yes there are cheaper routes of accomplishing this but we have had many go the cheaper route of going to a repair shop or attempting it themselves only to realise that something else has been damaged in the process. (Wifi cable is broken, areas of the screen that will not work, home button damage). There may also be other damage within your iPad that you may not be aware of as yet (I assume that the broken screen was caused by a drop)
If you do elect to go to Apple, make an appointment with the Genius Bar first and do a complete backup of your iPad, receipts are not needed as they can look up all relevant info instore.
Good luck!