The BMCC can't be operated properly without its LCD touchscreen. Most of the camera's features are controlled via the touchscreen graphical user interface.
If your camera's LCD is broken, get it repaired by Blackmagic Design.
If you want to send it back to Blackmagic, they are going to ask you to pay for shipping to them.. I had the same problem with one of my cameras, it's more economical just to return it to the store you bought it from.