Just in case it might be of use to someone, here is a photo of my "problem child" C860 with the display back removed.

The backlight had started to cut out intermittantly again, but this time I got my camera ready before the surgery began.

I suggest removing the 4 tiny phillips screws on the "bottom" of the display half (two one each side) before removing the two on the "sides". There is a small "lip" on the "front" (top) of the back cover that hooks into a groove in the other half, so lift the "back" (bottom) of the back cover first then slide it slightly "up" to disengage this "catch".

Can be easily put back together in reverse order. The cable connector on the top right of the picture is the one that keeps working loose on my machine and appears to carry signals from the "Base" (keyboard) part of the clamshell to the display section.