This is a strange one. I fired a Process Monitor and checked which files Divinity is trying to load. There were many PATH_NOT_FOUND messages and all of them were for files in steamapps folder, which is the default Steam installation folder in Program Files. However my folder was named SteamApps as Steam names it, when you specify a different library location. The problem is that Windows' NTFS is not case-sensitive, so this shouldn't really matter. As strange as it sounded, I still decided to reinstall D:OS in its original location in Program Files (x86)... and voila - the game works and characters follow.
Hope this helps someone.
P.S. I also cleaned up the D:OS folder in Documents.
