LCD Panels are very dark and thick: you need a powerful halogen lamp in order to see the fingers through the panel, and eventually fans to dissipate the heat in the box.
It doesnt need to be that bright to see the actual image itself though, without the back cover on you can just hold them up to a normal strip light and you can see the image fine.It could possibly be done with a 'cool' backlight for the screen, (like white UBLEDs, or a normal striplight with the box painted white)
but in addition to the lighting, use an INFRA-red camera/filter for detecting the fingers.