If you are not using Crimson 22.214.171.124 already I suggest you give it a try. Ensure you run DDU (Display Driver Uninstaller) in Windows safemode beforehand with any new driver install.
CrossFire does not activate in any other screen mode apart from exclusive fullscreen, so if you're running an application or game in windowed or fullscreen borderless window mode your second card will not activate.
Whilst troubleshooting, disable the overclock on your CPU if you have not already done so and revert any other non-standard modifications to stock.
I would also advise against using Furmark. In my opinion, it's akin to abuse and stresses your cards to a point you will never push the card in real-world usage. Rather test by running 3Dmark in a loop or any of the Unigine benchmarks. Even a graphically intense game such as Crysis 3 is a better option in my opinion. To gauge GPU usage, temps and framerate within a game, I've found CAM to be very low resource easy to use utility (No need to create an account, it still works without one).
Yeah, I got 126.96.36.199 today, but still got the same problem, and as I've tried 16.3.2 I don't feel as like it's a driver issue. And yeah I always use DDU in safemode.
I haven't overclocked my CPU anything at the moment, everything is stock.
The reason I wanted to try FurMark was to test the cards, to se if the same thing happened there as in BF4, since I've tried the heaven benchmark before and that seems to work fine. I wanted to see if the problem was related to power consumption/load. The strange thing was that as soon as I activated the FurMark benchmark I got the BSOD, not like in BF4 where it take some seconds before it freezes...
So I don't really know what to thing, I've tried everything I could think of except switching the cards to test the second card, but I doubt that is it.
Anyways thanks for your answer!