If the reset doesn't work, you may have to force iPad into Recovery Mode:
1. Turn off iPad. Press and hold the Sleep/Wake button for a few seconds until the red slider appears, slide to turn off.
2. Connect USB cable to computer; leave the other end alone
3. Press and hold the Home button down and connect the docking end of cable to iPad
4. Continue holding the Home button until you see the "Connect To iTune" screen
5. Release the Home button
6. Open iTune (make sure you have the newest version of iTune)
7. You should see "iTunes has detected an iPad in recovery mode"
8. Use iTune to restore iPad
Note: You need to be patient and repeat the above many times to recover your iPad
Just a heads up on recovery mode and restore, that will erase all data on the iPad, just a warning. Not much you can do, because of the state it is in. So the only resolution is to recovery and restore.
if you had back ups, use these links
I would try icloud first, because you can only restore from back-up using icloud during setup,
and if there is not and icloud backup then use itunes to restore from back up,
if you do not have any back ups then the information is lost.
but this link will help for the future on how to back up your ipad mini.
hope this helps.