By "tried to charge it and turn it on" do you mean for an hour or overnight?
The first hour or so of charging an almost totally dead battery doesn't give it much more power than to turn the device off. Leave it on the charger at least overnight, then see what happens. (The LEDs that light the screen from the back take a LOT of power.)
You might also need a new battery before long. Letting a lithium battery die almost completely (if it dies completely it's scrap, because charging a dead lithium battery can result in an explosion, so the last thing the battery does before dying completely is kind of blowing the fuse that connects it to the terminals) shortens the life tremendously. Never let it fall below 40% if you can help it. For long-term storage, let it drop to 40%, and check it every couple of months, topping it back to 40% when it drops a few percent.