Ugly dark shadows on character model, Skylight doesn't work

The Sky Light captures the distant parts of your level and applies that to the scene as a light. That means the sky’s appearance and its lighting/reflections will match, even if your sky is coming from atmosphere, or layered clouds on top of a skybox, or distant mountains. You can also manually specify a cubemap to use.

Sky Light | Unreal Engine Documentation

Skylights usually only work when there is a skysphere or HDRI backdrop in the level. It says here that you can try a manual cubemap as well. Do you have a skysphere in your level?