I got around my Black screen issues
I feel your pain as I too suffered the black screen issue when I first tried this game.
Although I was feeling more upbeat this morning when I finally got into the game, I've yet to actually try playing it.
In the hope that sharing my process may you/help others.
Obtained a key from online key provider - activated in Uplay and downloaded overnight (not the fastest internet where I am!)
Had black window with farcry4 logo top left - would never go further and had to end task
Tried to verify files - found approx 1gb of data and downloaded what it needed
problem still existed
Updated all system and Nvidia drivers
problem still existed
found some threads discussing USB peripherals.
disconnected the Xbox controller - same issue
disconnected my Razer Orbweaver - ooooo now I get to the loading screen...bar progress and some funny coloured balls floating across the background.
But the progress bar only gets to 'two thirds' then stops...have to end task.
updated the razer software - same 'two thirds' issue
removed the razer software - same 'two thirds' issue
tried swapping my razer mouse for a logitech one - same 'two thirds' issue - other than KB/Mouse - nothing else USB plugged in.
When I installed the game I was a bit worried about the space on my C: boot/OS SSD and had changed the install location for both the 'installer' and 'game' to my data drive (D: in my case, pardon the pun)
Checking the 'installer'/cache location - thought it strange that it was empty?
Checked the registry and couldn't see an easy way to change/hack the installer location back to C: - boo.
As I use Steam and had other Ubisoft titles in there I checked the C: location for the installer cache - which had files in it.
Something amiss with the change of installer location? maybe an issue with having Steam Ubisoft and just Uplay Ubisoft titles installed and the different locations?
Verified the files again - this time 14gb to download!!
Decided to take the pain and re-install the lot!
This time I set the 'installer' path back to default and only changed the game install location to my data drive.
Left to download overnight and this morning I could finally get past the 'two thirds' to the game screen. Had to leave to get to work :)
Hopeful that it'll work tonight. (not tried plugging the orbweaver back in yet either)
Good luck.