Try starting the game directly from the ..\SteamApps\common\Divinity - Original Sin\Shipping\EoCApp.exe program file. Perhaps right click and run as administrator (or right click, select properties and switch to the Compatibility tab if that doesn't help).
Are you shutting down all non-essential programs (especially anti-virus) before starting the game?
Did you check to make sure your firewall isn't blocking the game? (EoCApp.exe and SupportTool.exe both need access)
