Is it the black shape you are on about?
You can see there are 2 gaps in the path.
Join anchors at each side of each of them. (Either with the Pen tool or by direct selecting the anchors and Object > Path > Join)
The buttom paths is open, the top one isn't. I'm getting the error that both paths have to be on the same layer / group to join. In that case I put them on the same layer and group, and try to join them, they don't join. How do I make the top path open ? I've tried scissors, the knife, the knife works except it causes the part (right side of the image) to become a closed soild, which I want to remain open, as seen in the image.
One of the Anchor Points may have a double.
You can click each of them with the Direct Selection Tool, move it by a certain amount (so you can move it back) to see, and delete the end point or use the Delete Anchor Point Tool to delete the other one.
Like Monika says, it’s difficult to know what it is you want to join.
Do you want the black area to be continuous?
If so, Scott’s suggestion is good; Draw a black shape with the Pen over the bit you want to join, then select all the black stuff and Pathfinder (panel) Unite.