Black zones of zero weight insist in showing in my model no matter what I do and they don't move at all. What am I doing wrong? After skinning the model the same black areas keep showing. They do not move with the armature. I ctrl-J prior to skinning and still acts like it's not there! Can anyone help?

I worked with maya before and Blender is super new to me. So I don't know much about it but I got this far. I am doing this for work. confession: I brought this model from daz, and maybe that's why I am facing this geometry problem. 

What's weird, is that I was able to fix it before in another model. I think what I did was painfully select all the black areas in edit mode and added the vertexes to a group. I was wondering, if I select those areas in edit mode, and add them to the root, will it be seen in weight paint? I don't want to do that, but if I have no other option...

I tried to get several screens
I found a solution: the blend on "add", then I painted the black areas in one of the upper bones in red (1.0). I guess in other words no weight had been assigned to those vertices and once I did, those parts move with every bone.