Sorry to disappoint: Yup, you still need an active adapter.
You can only connect two non-DP screens (vga/dvi/hdmi in any combination of two) to your videocard. Anything above that needs to use DP (native DP or with the active adapter).
Of course if you have a screen that supports DP, use the two dvi ports and connect the third one from DP to DP. THEN it will work fine.
Bottom line is the first two screens can be connected however you want, third (and greater) screen needs to use DP, if the screen doesnt support DP you need an active adapter.
By the way, i'd try connecting the screen that doesnt work now without the other two screens first to see if it works. If it doesnt work that way, it's your screen that's broken, not the adapter. Worth checking out before shelling out the money on a pricy adapter to replace one that might not even be broken