I have scavenged several more LED strips from LCD's that have came through the shop and I've gotten a few that are on flexible PCB which are -not- covered with silkscreen to protect the traces/design.... I pinned one out and it looks like its pretty simple, at least on that one.... I've attached a schematic to show how its wired up.
I've also found an IC that should work for lighting these strips up which is available from Digikey.
Intersil 6-Channel SMBus/I2C or PWM Dimming LED Driver with Phase Shift ControlISL97671A <- PDF
ISL97671A on DigikeyI like the fact that it has I2C control for dimming as well as device control/status but at the same time I would totally be over my head for making a program sketch to communicate with it. The PDF has some pretty good information though regarding communication. I just don't know enough about I2C...
If someone was
seriously interested in helping figure out how to use this Intersil IC with Arduino and how to get all the control and status feedback working I could send you a LED strip to test with...