Are you shutting down all non-essential programs, not just anti-virus)?
Firewalls have also caused startup problems with those symptoms (black screen, just the game cursor).
Try starting the game directly from the '..\SteamApps\common\Divinity - Original Sin\Shipping\EoCApp.exe' program file (or similarly for the GOG install path), by right clicking and running as administrator.
You could try temporarily lowering your desktop resolution, to limit what the game will try to start at, but if you didn't have a problem before, that shouldn't be an issue now without at least a driver update, or something.
If this started after the last update, or you haven't played since then, check the contents of your '..\SteamApps\common\Divinity - Original Sin\Data' folder; it should (in 1.0.219) contain an engine.pak and game.pak files, 3 main pak files and 3 textures pak files (and a text file). A couple people have had crashes on startup due to extra pak files in this folder; some were a case of a copied file (even with a different extension) made to try hex editing a main pak file, while one was apparently temporary files not cleaned up properly after an update.
For the Steam version, did you try verifying local files? In the Steam library, right click on Divinity Original Sin and select Properties, switch to the Local Files tab and then click on the 'Verify Integrity of Game Cache...' button.
Try browsing to the '..\Documents\Larian Studios' folder and renaming the 'Divinity Original Sin' subfolder.
This folder contains the saved games, configuration files and a level cache folder. Deleting or renaming it will get the game to recreate it on startup; playing the game from a different Windows user account would effectively do the same thing.
After that, see if you can start D:OS. If so, create a new profile and maybe check if you can start a new game and save/load. Exit and then you should just be able to copy your saves from the renamed folder into the newly created profile's savegames folder.
If that doesn't help, delete the new My Documents D:OS folder and rename the original back again.
If none of that helps, please email supportdos@larian.com, with a description of the problem (and/or link to this topic) and the report.zip file generated by the
D:OS support tool (for the PC version). The report will contain system and game information, as well as your saved games. To reduce the file size, you can delete all but maybe one of the saves.
Also, check the '..\Divinity - Original Sin\Shipping' folder for any CrashDump files, and either add some to the report.zip, or zip them separately.
