All these super techs on here with their posts.
O.P when you press your top botton and the windows come down and the top starts to go back and it stop basically the harness that goes through the left part of your tops frame is either cracked or cracking and it has to be rewired. If you look at in between the top and the frame right above the drivers side you will see a harness that goes through the frame. Since that wires goes through the frame and it pinches itself it usually cracks.
BMW sells the harness repair kit but you basically have to take the top off and change all the harness in that section. I strongly suggest you let an Indy shop or the dealer handle this since its a huge job.
Again since I havent seen the car I cant tell you if that is your problem, but for my past experince what your posting indicates that the harness is the problem.
The trunk latch wouldnt be the problem because if it was then the windows wouldnt roll down and the top wouldnt move at all.
It also can be the micro switches on the rear sides of the frame as well, but an scan with a GT will tell you if micorswitchs are bad. I would start by looking at the wiring harness first.
At least if that is the problem then that saves you some diag money.
Let me know what you find out. Also you can P.M if you have some questions.