I have the exact same error.
I'm running a HD6950 (Sapphire flex edition) and the onboard HD4290 on my Gigabyte GA-890GPA-UD3H mainboard.
The Problem is that I can't seem to find any way to drive the two correctly simaltaneously.
The two options are what culhy described. Both cards can be used in Windows (effectively letting me drive 4 displays) and some games/renderes will run, but most will crash immediately (including CCC). This is the case when you first install the driver for the HD6950 (13.9 in my case) and then the one for the HD4290.
The other possibility is to first install the legacy driver for the HD4290 and then the newest driver for the HD6950. In this case all games, renderer and CCC will work, but the onboard HD4290 will completely stop working. It will always "crash" when activating it in the Device Manager with the error code 43. Obviously I cannot use any monitors attached to the HD4290 in this case, letting me only use 3.
Whenever I force Device Manager to use either the legacy driver or the HD4290 driver that comes with windows, it will reset back to the first case (not letting me run any games, CCC crashing etc.)
Is there any way to get both cards to work at the same time? Because this problem is really beginning to annoy me!