The backlight of this Canon PowerShot sd400 doesn’t work anymore, but the rest of the lcd is fine:
I can order a new backlight for about $20 via eBay. The old one is worthless now, so I had a look inside. It disassembled into several layers:
On the left is a stack of thin plastic sheets that form the topmost layers of the backlight. They serve to diffuse light from the layer below.
On the right is thick plastic layer stacked on top of a reflective metal backing. Three tiny leds are affixed to the right edge of the plastic layer and shine directly into it from the side. This layer turned out to be birefringent with some curious optical properties:
You can see its purpose when the laser shines sideways into its edge. The whole surface lights up evenly.