ATI catalyst never was friendly to this game i could honestly say that cause since 2005 i have played on X1650,2600XT,HD3650,HD4850 and last 3 years HD6850.
Since 9.1 version till updated 13.x they didn't made much progress,ironically some options in Catalyst Center were disabled or made game total unplayedable...with low FPS,Shader or Vertical sync problems
As you said all other games runs smooth instead of just GTA:SA
On many webpages you can find similar posts to this one
I find this strange but, Catalyst 12.8 is kindoff faster than the 12.9 and 12.10?? the difference are on the FPS,,, is there anyone having this?? I have an Powercolor hd6850
Solution exist but you must be patient to find what you looking for.
Easiest way is to completely uninstall Catalyst Control Center and ATI drivers in general and give try to Omega Drivers, they run fine without MS Framework so it will use less resources on your PC which result better performance and probably decent FPS on this game. (I am not 100% sure there is support for your model cause website has been down in moment when i checked support list)
Or if you want play with CCC drivers try some older version as 9.8, 10.3, 11.12 or some what match with your model of card...12.6 is latest designed for 4xxx series
Its been long time ago since i sold my 4850