My PRS-505 experienced death by Airborne, the herbal remedy "Invented by a school teacher". I spilled a glass of it on the 505 and while the unit survived the battery's chemistry was neutralized (most likely by the calcium carbonate from the drink) and now it no longer holds a charge.
Since the battery isn't user replaceable I've put it in the museum next to my Libre (which suffers from a broken battery compartment) and my iLiad (which suffers from incredibly poor design and corporate ethics).
The Kindle has a user replaceable battery so you can self repair it from this kind of damage.
I recently bought a Segway and my Kindle pulled the scare the owner into thinking its dead trick. Which was doubly convincing for me since I figured I'd killed it riding the rough sidewalks around here. What I add to the otherwise complete Kindle recovery advice given above is: make sure the unit is charged.
The 505 and Kindle both appear dead as a door nail with no gas in the tank.
By the way, the Segway was indeed the culprit. Seems the Kindle's battery can be quickly run flat by pressing the buttons, when its in alt-aA mode. I now keep my Kindle switched off in the Segway's handle bar bag's zipped net pouch and all has been fine since.
And for those with "buttery fingers" I've found its generally harder to drop the Kindle or knock it off tables because of that big pad of high friction rubber on the back.
If you had visions of it landing rubber side down for a softer landing? I can report from personal experience that Murphy, or physics, seem to dictate a screen side down landing. I've had it fall twice from 36" onto a hard tiled concrete floor and pull through both times. And as I mentioned, it rides everywhere on my Segway, which is a hard ride at times.
If the rumors are true about who builds the Kindle for Amazon... Lenovo/IBM... that firm has near legendary status for building durable hard to kill portable equipment.