In the viewport under lighting, you can double-check the two-sided lighting option box is turned on. You may be viewing a backface. If you are, it will display as solid black. The other option is you don't have any lights aimed at your object.
"other places where light does not directly hit objects", the viewport is not a render engine, it does not calculate bounce light. And hardware in 2014 is a really obsolete viewport. You need to adjust your lights and materials to compensate. If this is just for preview then it doesn't matter, add fill lights like ambient light (horrible light if you plan on rendering). If you do plan on rendering your scene later, set it up to look good in render and not in the viewport. The two will not ever match.
Let me know how it goes.
