Screen turns on. But turns off later.

Why did you put it in rice?

If your iPad was in contact with water, then you need to have it cleaned asap before it dies completely. You could try this yourself seeing as how the shields do not have to be de-soldered.

• Open your iPad and remove the logic board (follow this guide)
• Inspect the logic board, especially around the connectors and look for corrosion.
• Put your board in a container with >90% isopropyl alcohol and let it sit for a while.
• Use a soft brush, like a toothbrush and lightly brush away any corrosion you see.
• Rinse in alcohol and repeat.
• Let it air dry for a day.
• Re-assemble and hope for the best.

A professional repair shop that does water damage repair may be able to recover your device or the data because they have access to pro-level ultrasonic baths and specialized cleaners as well as the skills to troubleshoot your board.