It seems your LCD is broken . That's what this "square" issue is. The LCD lies underneath the glass that serves as touch screen.
Here's the guide for replacing the LCD. It also has links to the needed parts and tools.
Since th e outer glass is also broken, you will ALSO need the "front panel digitizer assembly."
You can buy only the digitizer assembly. Use the guide to remove the broken digitizer. When you get to the LCD, disconnect then reseat the cable of the LCD (gently, those have very fragile connectors). If reseating doesn't solve the "square" issue like you call it (I doubt it will), then order and replace the LCD before re-sealing the iPad.