Could be anything from misunderstanding how nested comps work, specifically continuous rasterization/ collapsed transformations onbly using the parent comp lights, to the usual issues with hardware acceleration to the simple fact that such a dark source may require you to create an extra ambient light in the comp and/ or tweak the material properties. Unfortunately you cropped away the critical timeline info, so we can't tell you more than that.
If you have 3D layers in a nested comp (pre-comp) you have to turn on collapse transformations for the lights and camera in the main comp to work on those layers. That's the most common error.
The second most common error is making sure that the lights are actually pointing at the layers. The third most common error, improper settings for lights, and material options for your layers. Find the material options by pressing "aa" and checking the settings.
Your cropped screenshots are pretty useless except for the fact that I don't see any layers visible under the current-time indicator except the top layer.
Please embed your screenshots using the toolbar. They are a real pain to look at when you have to download them.