Assuming one has a complete burn operating setup (no visible fire for about two inches from end of grate), what appears to be unburned coal can be two things:
1) Unburnable slate material. This is dark in color and looks like coal, but it crushes like rock. It's really an indicator of the coal quality.
2) I have heard that "Banked" coal also will not burn. (I haven't personally seen it though, so I can't confirm). Years ago I'm told, the smaller fines (rice and pea) were not of use, so they were "Banked", piled up and left on the side. So the story goes, the banked coal is now being mixed in with freshly mined coal. After being banked for 75 years or so, all the volitiles in it have evaporated.
For what it's worth, I'm not sure I buy the banked coal explanation for unburned coal. I think that the grate design of all stokers I've seen are capable of burning pure carbon.
Maybe the Coalman can shed more light?