EmbrosCyan: It looks like the game is crashing
In the Event Viewer, did you sort by Date and Time to look for a recent error?
Are you shutting down all non-essential programs (especially anti-virus) before starting the game? Firewalls have also caused conflicts.
Try verifying files, if you are using the Galaxy client: select the game in the left column, then click on the More button, and in the Manage menu select 'Verify / Repair'.
Try renaming the intro.wmv and loading.wmv videos in the '..\Divinity 2 - Developers Cut\Data\Video' folder. That may avoid a startup crash.
Try starting the game directly from the 'bin' subfolder of the main install folder: Divinity2.exe is the normal mode, while Divinity2-debug.exe has the optional 'Developer Mode' cheat menu. Right click either the executable and run as administrator.
PhysX is one of the more common causes of crashing on startup, though in that case generally before the initial splash video. You could try installing the latest version, though. You can also install the version that comes with the game (in the support folder); you may need to uninstall the current version and reboot first. If that gets the game to start, you should then be able to update to the latest version of PhysX.
You can also reinstall the other support packages in the install folder, MS VC and DirectX 9c (the latter does not come installed by default in Windows 7 or 8; it does for Win 10), though the installer should have already done so.
Check for updated drivers and Windows updates.
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, then click OK and reboot the computer.
Run msconfig again to switch back to the normal boot configuration.
You could try setting a lower game resolution manually by editing the file below in a text editor, and/or put the game into windowed mode (unsupported) by changing the one to a zero in Fullscreen="1".
C:\Users\<UserName>\AppData\Local\Divinity 2\Profile\graphicoptions.xml
You may need to set Windows Explorer to show hidden files and folders:
http://www.howtogeek.com/howto/windows-vista/show-hidden-files-and-folders-in-windows-vista/
(covers Vista through Win 10)
If that doesn't help, check out the suggestions and links in the discussions / topics below:
Game won't start Game won't start, I need help desperately Divinity II Crashing on Startup (avoided by using
DxWnd; the problem didn't reoccur after they switched to using a monitor, rather than a TV)