Hmm, very sorry to hear of the troubles you are having. If I had to guess, I would usually say that it's a gamepad or similar that is causing the issues. The fact that you can click in menus is awfully suspicious, though. Are there any error messages in the RuntimeData folder inside the game folder?
On a related note, the fact that you had to set the execute bit is very surprising, as well. The zip we provided to Humble had that set, I'm pretty positive. I did it myself. I'm not sure why it didn't unzip with that set for you. :/