This is not an official solution yet, as we still have work to do on this, but let me give you an update on where we are with this:
We've managed to reproduce problems reported by messing around with the video codecs. We're still trying to figure out exactly what situations can cause the problem, but it's clear that it can cause problems for Divinity 2, and it explains the never-ending loading screens we've seen reported which up to now didn't occur in our office. Your message was actually the trigger we needed, so thank you very much for that !
The ffdshow question was inspired by a bug we saw reported for Fallout3: http://www.google.com/search?q=ffdshow+fallout3&rls=com.microsoft:*&ie=UTF-8&oe=UTF-8&startIndex=&startPage=1. The steps suggested might solve your problem, but perhaps not as you already uninstalled ffdshow (but traces might indeed persist).
We've discovered that for some odd reason, different codecs were used in the compression of the videos used by Divinity 2. We further discovered that even if they play correctly in Windows Media Player 9, the video playback mechanism in the game doesn't necessarily manage if there's a problem with the codec.
On the machine we managed to reprodce the problem on, this is what happened:
With Windows Media Player 9 the movies played correctly BUT the game didn't render it and hanged as a result.
We installed Windows Media Player 10 and tried to load the same movie. This time, Media Player asked us to install a codec as apparently it couldn't find it. When we allowed it to install the codec, the game ran fine.
Our QA is now checking all the movies, and seeing under which circumstances problems with a specific codec can cause problems with the game. This will take them some time, but once that is done, we should be able to point out which codecs you need to download to make the game run.
I recommend waiting until we've clearly isolated the problem, but if you want to try something yourself, you might want to install the latest version of Media Player, and try to play the movie that's causing problems to see if it now asks you for a codec. If it does, installing that codec should solve your problem. Alternatively, you can try replacing the video that blocks you with the intro video (which I guess you could see) as a temporary workaround.
Thank you once again for posting here and pointing us in the right direction.