Fill color won't fill everything selected

Looks like you have drawn corners by 2 lines each one (horyzontal+vertical) and many separate short lines between the grid points. So you don't have any closed objects. Corners are filled by connecting the path endpoints with the shortest way (diagonal line), but other grid elements are just lines, not fillable at all. 
So now you can only do what Monika suggests: select all the grid cells and use the Live Paint Bucket tool (it is under the same button as Shape Builder tool)

Try and use Live paint to fill it.

It's not clear how the grid is constructed. If you can, please post another screenshot with all selected and the Layers panel in view.