Get:
1x REED type switch - normally closed.
1x Small permanent magnet
1x 2AA/AAA Battery Box
1x Red 5mm LED
1x Resistor 47 ohms (yellow-violet-black)
3x short lengths of wire
The magnet is attached to the front edge of the case; when its closed it keeps the reed switch open, thus the LED is off. It opens and the reed switch closes the circuit.
If you know basic electical wiring you can figure out the circuit yourself.
(just wire everything up into a loop, and pay attention to the LED's orientation -- wrong connection and the LED fries)
The hard part really is building this INTO the case.
Info all around the net:
http://led.linear1.org/
http://www.theledlight.com/ledcircuits.html
http://dansdata.com/caselight.htm
Have Fun!