Are you shutting down all non-essential programs (especially anti-virus) before starting the game? Firewalls can cause conflicts (generally on startup or loading screens) and overlays from graphics tweaking/monitoring programs or chat programs can also caused issues.
Try exiting out of the Steam client, and starting the game directly from the '..\SteamApps\common\Divinity Original Sin 2\DefEd\bin\EoCApp.exe' program file, by right clicking and running as administrator (or '..\Divinity Original Sin 2\Classic\EoCApp.exe' for the original release).
Try verifying local files: in the Steam library, right click on the game and select Properties, switch to the Local Files tab and then click on the 'Verify Integrity of Game Cache...' button.
With the GOG version, in the (optional) Galaxy client, select Divinity: Original Sin 2 in the left column, then click on the More button, and in the Manage menu select 'Verify / Repair'.
Try doing a clean boot and then test the game. Click Start, or hit WinKey-R, type in msconfig and hit enter; in the General tab, click Selective Startup, uncheck Load startup items (if required) and leave Load system services and Use original boot configuration options checked. Next, click on the Services tab, check the box to Hide all Microsoft services, then click the Disable All button (maybe make a note of which are currently enabled/disabled), then click OK and reboot the computer.
Run msconfig again to switch back to the normal boot configuration.
Try browsing to the '..\Documents\Larian Studios' folder and rename or delete the 'Divinity Original Sin 2 Definitive Edition' folder.
This folder contains the saved games, configuration files and a level cache folder. If the game was working before and you have saves, rename the folder, otherwise if you don't have any saved games, you can delete it.
Next, extract this
replacement folder into your '..\Documents\Larian Studios' folder, and see if that will let you start the game.
The graphicSettings.lsx file is set to 1280x720 Windowed mode, Very Low quality preset and low audio quality, which you can change in the options (manually, or hit autodetect) if this gets the game to start. This also contains an extra option not set in the download in the support topics (which I still need to update), which can help for a particular issue if the DE crashes but Classic is ok.
If that doesn't help, please email supportdos2@larian.com with a dxdiag report (WinKey-R, type in dxdiag and hit enter, then when it finishes loading click on the 'Save All Information...' button and save the report somewhere handy). Also check the '..\Divinity Original Sin 2\DefEd\bin' folder for the gold.log file, and if any 'CrashDump' files are being created, zip a few together to include.
