I have the same problem but got it on a different way.
I did not know that's possible to use the cable of BD-1's jail as a liana. Because of that I did not connect the cable with the energy port above his door and thought to find maybe a way to release BD-1 by using the elevator. Arrived in the next floor I followed the tunnel and has fought in the arena. After the battle I was rescued and... now I haven't BD-1 anymore and would also like to know if there is a workaround to get him back. Maybe a save game reset or something like that.
For know, I expect that's not possible to continue with the game...
i did the same as you as i was stuck figuring out the puzzle i didnt even know tha was an elevator. now im stuck.
