I've tried so many times to run "Black Mirror" after I started using XP but everytime I got this black screen at the start up. I've bought the original version with Bulgarian subtitles and it wasn't until half an year until I found what was the problem. You must download a patch from NVIDIA and put it into your game directory. Afterwards, install it and enjoy the game.
Here's the link to the NVIDIA patch:(click)
NOTE : This patch is for the Bulgarian version so I am not sure if it will help any other versions but you can try it anyways. Also, I have only tested it on an NVIDIA graphic card. The Bulgarian version only has Bulgarian subtitles and English audio, so if you can't run your current version, you can try finding the Bulgarian one and play it instead. You can register with Zamunda and download it from HERE. Enjoy!