I had a rather upset client come in the other day with their newly-broken Kindle Fire. While he didn't know what had actually happened, he suspected that it had been dropped once or twice, as it sounded like a maraca when you shook it. After some reassuring words, the client parted his beloved tablet returned home to patiently wait. In the meantime...
The first step in any successful tear down is to, well, tear down! After a quick inspection and a few minutes of research, I discovered that the Kindle Fire is relatively easy to disassemble, and can be performed using nothing more than a small Phillips and a small Standard screwdriver.
To begin, find a soft spot in the seam along the edges and work the small standard screwdriver under the back cover.
Gently work your way around all four sides until you break the back cover loose.
(close up of the internals)
After removing the back cover, the next task is to get the battery out of the way, which is generously glued in place. Use your screwdriver to work the battery free. Do NOT crush/fold/puncture/tear the battery back! It looks like metal, but feels more like clay ("battery acid") wrapped in aluminum foil ("aluminum foil").
Once the battery pack is out of the way, continue removing whatever screws you can get to until the motherboard comes free. After all of the screws are removed, lift up on the side opposite the USB port to detach the motherboard from the chassis.
If you have made it this far, the final step in a complete tear down of the Kindle Fire is to remove the last remaining screws and separate the LCD screen from the front glass. After doing that, your Kindle will look like this:
With this Kindle Fire, the problem was indeed that the device had suffered some blunt force trauma on one or more occasions. I found that (aside from having one loose screw floating around inside) the ribbon cable connecting the LCD display to the motherboard had come loose. After reattaching the display and a quick reassembly (read this guide backwards for re-assembly instructions), the device started up without hesitation.