In the world settings, do you have "force no precomputed lighting" enabled? Did you re-build the lighting after enabling that option. That removes existing baked lighting. Also, what happens when you crank up the skylight intensity?
If the skylight is movable, assign a cubemap to. Otherwise, it will only use a single color which will evenly lit ambient lighting. Using a cubemap can yield more realistic result because the cubemap texture will have different stuff on its sides. For example, it can have some directionality from the sun being on one side…