I want to make an LED light for my Kindle 3. I really like the Kindle, the heavy Amazon cases, not so much, I bought a Built neoprene case instead. So I missed out on the light and I now think it would be useful to have one for reading in bed.
The video teardown and photographic teardown give quite a bit of general detail. The hinge is well photographed in photo 31 of the techrepublic teardown, see below. The JTAG headers and RFID chip are also interesting, but I'm keen on making an led light.

Photo credit: Bill Detwiler / TechRepublic

The hinge detail from the Amazon website.
Mike Harrison has more detailed notes on the serial interface pins and how they might work, plus some clear photos of the connectors. He has a full listing of the boot console messages which come over the serial port.
Photo credit: Mike Harrison
Next step is to look at a Kindle lighted case and see how the electrics work on that. I think that Mike is right in that the complex connector is used for setup prior to dispatch, the video teardown alludes to this too. When they dispatch the Kindle it is part charged and configured for you using the electrical interface below. Drop in, configure and pack into the box and dispatch.Somehow though the combination of the two connectors provides power to the light circuit and it seems that there are just two electrical connections, one at either end of the hinge mechanism, as you can see above. Looking at the layout of the hinge connector and the open PCB it seems that the four connectors on the left will not make electrical contact with the hinge connector. The two connectors shown on the right of the first image seem to be the ones which make the circuit with the clip like connector on the top. Next to take one to bits and compare it with the lighted case. This large internal shot of the Kindle 3 (Credit Blogkindle) shows the mechanics of the hinge well.
Building Social Web Applications by Gavin Bell.