Have you tried starting the game in steam? What worked for me was launching a mission using the steam version of the game and then try to activate the game with DCSW. After that I applied this patch and the activation in DCSW worked. Hope this helps. :)
I have a very similiar problem. I also bought the game from steam, but I started the steam version before installing DCSW and the A10C module. The steam version works fine (duh), but DCSW version won't authenticate and I keep getting this screen: