Have you been able to run any other DirectX 9 games? The problem with the Analysis Tool result may be an issue with a change in how Win 10 reports the DirectX version, rather than a problem with DirectX itself.
In the 'C:\Windows\SysWOW64' folder, check if there are DirectX 9c files present already, such as d3dcompiler_43.dll, d3dx9_43.dll and xinput1_3.dll.
Check the Event Viewer, and see if it gives an error code or 'Faulting Module' file name, which might help identify the cause of the crash.
- click Start (or WinKey-W in Win 8; may have been carried into 10), then type "event viewer" (just "ev" works in 7/8) into the search box. With Win 10, that 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 (maybe sort by Date and Time) for the game
- check the information under the 'General' tab below the list of events, starting with "Faulting application name..."
Did you try renaming the 'Divinity Original Sin' subfolder in your '..\Documents\Larian Studios' folder, to get the game to recreate on startup? If so, do you recall if the game recreated the graphicSettings.lsx file, or the PlayerProfiles folder before crashing?
If you didn't try that, if applicable, first disable 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 and select Properties, then switch to the Updates tab and check the Steam Cloud section).
