What you're actually getting out of that is something almost exactly like this, which can be bought fairly cheaply and in bulk if necessary. The expensive movie version of this is the Arri Versatile, which is exactly the same thing, just with more carefully-selected LEDs. The low-cost LED ceiling panels were used as practicals on the TV series Critical, built into the set, where they were deliberately selected to provide a cold, cyanish glow in the background. Versatiles were used as properly coloured keys.
The problem with the cheap ceiling panels and recycled monitor backlights is that the colour rendering will be absolutely horrible. Office lights are built for maximum output, not good colour rendering, and monitor backlights are designed to match the dyes in the display panels they're used with. Neither is likely to produce colour suitable for use as a key light, although I'm tempted to grab one of those low-cost two-foot-square things and see if it can be pressed into service, perhaps with better LEDs.
The other problem is that none of this edge-lit panel tech, no matter how good the LEDs, is really all that efficient. The diffusion required to create a clean rectangle of light from an edge lit device results in a lot of absorbtion in the acrylic panel itself. Even though it's optically quite transparent, the light has to go through whole feet of it, and many lossy bounces, to get to the middle.
It's interesting and has application because it's very shallow - the ceiling panels are under half an inch thick. But it's not really the best approach imaginable.