Black screens can be caused by a number of things, but mostly video card or display drivers. There's at least one known issue listed related to a black screen (details below). That said, if you haven't done so, make sure you install the latest display drivers for your video card and send in the dxdiag to support if you haven't. It'll help us tackle where the issue is coming from. Going to move this over to the community support forums.
[PC] Game stuck on Black Screen
- For the users affected, the game would get stuck on a black screen on startup. After disabling the Uplay Overlay in the Uplay PC client via Settings->General-> uncheck "Enable in-game overlay for supported games", these players were able to start the game. We are currently trying to reproduce this problem and are working with the Uplay PC team to find and fix the issue as fast as possible. You can help us by contacting customer support and sharing details on your hardware and software configuration, for example by sending your DxDiag report, in case you encounter this issue as well.