screen frozen in ON state

The thing about those e-ink displays is that they don't require any power whatsoever to maintain the display, so they're not like a cell phone where you can tell it's off because the display is blank; the kindle display won't ever go blank from not having any power.

So at this point you don't know if it's a dead battery, a broken touchscreen or a malfunctioning charging port. Does it have any LEDs at all to tell you it's on or not? Does it vibrate when you turn it on or off? Is it recognized when you plug it into a computer?