I'd try the reset button as Seabound suggests.
Just wanted to add, that even when the screen is "on" your reader shouldn't actually using much power. With e-ink technology, it doesn't take any power to keep the screen on. The reader should only be using power when re-drawing the screen.
Sounds like you probably have something else going on. Could the audio player be on in the background?
Hopefully the reset will fix your problems.
dordale