This is my laptop; a Panasonic Thoughbook. A nice P3-750, which is a bit slow for todays multi-GHz-world, but it does the job and it hasn't cost me an arm and a leg. Whem illuminated by the camera's flash, everything looks OK, but when we turn off the flash...
...it's clear the keyboard isn't readable anymore.
To fix this, we need to open up the laptop. I'll save you the finding of hidden
screws and snap-connections; sufficient to say that eventually I could
remove the border around the screen. There is enough space there to put a 3mm LED.
For the proof of concept, a white led is connected to a power supply through a series resistor. The led does seem to generate enough light to let the user make out the key caps. The following pic is taken without flash in a dark room:
After drilling a hole, the led can be placed in it facing downwards. To get the angle right, it's helpful to put a drop of hot glue on one of the pins of the LED and get the display-frame roughly in position.
After checking out where the leds light goes and eventually adjusting the leds angle, it can be fixed in place with a larger drop.
If you're not that technically inclined but do want to build your own Thinklight-clone, please consider stopping at this point. Just get yourself a switch and a place where you can tap 5V in the laptop, connect these in series with a current-limiting resistor, and be done with it. The solution I built for my light is nicer, but quite a bit more difficult to get right. Just so you know.