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.
Try right clicking the executable, select Properties, switch to the Compatibility tab and check off the 'Override high DPI scaling behavior' option (set it to Application), maybe run as administrator and disable fullscreen optimization, and set a Win 7 or 8 compatibility mode.
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.
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'.
If you check the Event Viewer, does that give an error code or 'Faulting Module' file name that might help identify the problem? It probably won't with a freeze like this, but it couldn't hurt to check.
- click Start (or WinKey-R), then type "event viewer" into the search box. in Windows 10, 'event' should bring up 'View event logs'.
- after starting the Event Viewer, expand 'Windows Logs' in the left column and select 'Application'
- in the center column, look for a recent error for the game (maybe sort by Date and Time, or search for 'EoCApp')
- check the information under the 'General' tab below the list of events, starting with "Faulting application name..."
If applicable, disable Steam cloud support either globally (in the client click on the Steam menu and select Settings, and then Cloud) or just for this game (in the library right click Divinity: Original Sin 2 and select Properties, then switch to the Updates tab and check the Steam Cloud section).
Alternately, exit out of the Steam client, or Galaxy for the GOG version, and just start the game directly from the executable when required.
Next, try browsing to the '..\Documents\Larian Studios' folder and rename the 'Divinity Original Sin 2 Definitive Edition' 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. With Steam running and cloud support enabled, the client would just download the cloud copy of your existing profile.
After that, see if you can start D:OS 2 DE. If so, create a new profile and maybe check that you can start a new game and save/load. If that works, exit and copy a couple saves from the renamed folder into the newly created profile's ..\Savegames\Story folder, if you have any from the Definitive Edition. If that continues to let you start the game and load the saves, move the rest of the saves over.
If a new folder doesn't help, delete the My Documents folder for the game again, and extract the replacement folder from
this download 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.
If the game still freezes, delete the replacement My Documents D:OS 2 DE folder and rename the original back again.
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, switch to that account and try starting the game from there, directly from the executable.