Your problem is more than likely a broken ground. I had this problem and it was fixed by running another ground wire around the dead section. I have a thread in this section as well as a couple of other members. For what I paid to have this found and fixed I could have bought a brand new wire harness for a lot cheaper ($150 for the harness)
Search for things like "top won't go down" in search.
Also as a hint, my wire broke right above the drivers door in the wire loom at that bend in the top (above the drivers door). When you have the drivers window down and the top starts to fold you will see the harness I'm talking about between the layers of roof.