From your description it sounds like the LCD has a large pressure mark on it. Is the middle of the display still responding to touch properly? If the display still responds to touch properly then you likely just need to replace the LCD panel.
You don't mention the generation / model of your iPad but repair is possible for all generations, the process and part cost will vary though. This particular repair IS quite involved for all of the models, I would encourage you to read and re-read the guides to make sure you're comfortable performing the repair before ordering any replacement parts.
For instance, a replacement LCD panel for a 3rd/4th generation iPad, the retina models, costs $99.95. iFixit Retina Display
This same LCD can be installed using the following guide: iPad 3 Display Replacement Guide
The parts and guides do differ from generation to generation so be sure to use the proper guide when attempting the repair.
Hopefully that helps!