How to save my app files and/or data from my iPad 1 whose screen won't turn on?
Connect the device to iTunes and force a backup using the menu command.
Restore that backup to another device and carry on with getting the files off.


You should be able to borrow someone's iPad for little expense (a few beers or buy them a Pizza) and then wipe your data once you're convinced you've exported all the data you care onto the computer or wherever it's going to live.