When it hangs, did you try exiting the game using Alt-F4?
Are you shutting down all non-essential programs (especially anti-virus) before starting the game? Firewalls have also caused conflicts during loading screens.
Try starting the game directly from the '..\divinity2_dev_cut\bin' folder: Divinity2.exe is the normal mode, while Divinity2-debug.exe has the optional 'Developer Mode' cheat menu. Right click the executable, select Properties, switch to the Compatibility tab and check off the option to run as administrator, and try XP compatibility mode, or something. One person in Win 7 reported getting past a hanging loading screen by switching to XP SP2 mode and disabling Desktop Composition.
Did you try changing graphics options, etc (in the advanced graphics options, maybe try disabling 'Use multicore' or enabling 'Lockstep mode').
You could try setting the game to run in windowed mode, by editing the file below in a text editor and changing the one to a zero in Fullscreen="1".
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)