Are you playing the original release or the Enhanced Edition?
Are you shutting down all non-essential programs (especially anti-virus) before starting the game?
Try exiting out of the Steam client completely, and starting the game directly from the '..\SteamApps\common\Divinity Original Sin Enhanced Edition\Shipping\EoCApp.exe' program file, by right clicking and running as administrator (or similarly for the original release).
You can try verifying local files, though reinstalling should have fixed any issues with missing or corrupt files, especially if you made sure the install folder was removed (or empty) after uninstalling, or installed to a different location.
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.
Try browsing to the '..\Documents\Larian Studios' folder and rename the 'Divinity Original Sin Enhanced Edition' folder.
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. With Steam running and cloud support enabled, the client would just download the cloud copy of your existing profile.
Next, extract the replacement folder from this download
there, to see if that will let you start the game properly.
The graphicSettings.lsx file is set to 1280x720 Windowed mode, Very Low quality preset, which you can change in the options (manually, or hit autodetect) if this gets the game working.
For the Classic version of the game, use this replacement folder
That graphicSettings.lsx file is set to a 1152x648 resolution, and windowed mode.
Alternately, you can rename or delete the graphicSettings.lsx file, to get the game to recreate it on startup, to see if that will get the video showing properly.
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 creating a new Windows administrator user account (with the My Documents folder on a different drive, if possible, or at least not in a One Drive folder, as Win 10 likes to do), switch to that account and try starting the game from there, directly from the executable.
You can email the dxdiag to email@example.com