Youre either going to have to pay someone to fix this, or replace it. That much is clea. For that reason, while the repair I am going to recommend sounds unorthodox, you can read in the comments section on this page where its worked many times before.
What you want to do is find a table.. Now, with the screen facing up. Lift the ipad about 6 inches and drop it flat on its back.. let it smack the table. ( screen facing up!)
Then, hold the sleep wake and home buttons and try to reset it and see if it comes on.
Worst case scenario, use a little force and bang it on the table.. It needs to be flat and screen up. keep in mind, were not trying to break it further, but just jolt it out of its current state. Try that a few times.. You may actually get it working!
If not, then you will need to consider a repair service such as this.
Good luck, and let me know if the above trick works!
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Senior Technician and Network Switching Systems Operator / Maintainer.