Sorry to hear that you get a black screen on launch. I would suggest to try running Steam and/or Uplay as admin first of all.
You can do this by right click the .exe files before launching them and choose the "run as administrator" option.
Also right clicking and choosing "Properties" then go to the "Compatibility" tab and ticking the box to "run as administrator" option and clicking "apply".
You can also do this with the games .exe file in the installation folder too and see if that force launches the game.