It sounds like a compatibility issue with the game rather than your hardware. The HD 6950 should certainly be capable of handling AA, but older games can sometimes ignore driver-forced anti-aliasing, especially when they use their own rendering method.
Since you've already tried both the in-game MSAA settings and forcing AA through Catalyst Control Center, I'd try creating a specific profile for NecroVisioN rather than changing the global settings. Make sure the profile is set to Override application settings for AA rather than “Enhance application settings.”
If that still doesn't work in either DX9 or DX10, there's a good chance the game simply isn't accepting the forced AA with those drivers. You could also try an older Catalyst driver, since 11.1a may have introduced or exposed a compatibility issue with the game.
Given that everything else is running normally, I wouldn't worry about the GPU or RAM. This looks much more like an old-game/driver interaction. Check out
fnaf to know more information.
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