I recently bought a Radeon ATI HD3850 to use in SL because and explicitly because it's on their "supported" list.
Numerous of us that have bought these cards have experienced crashes within a minute or two of logging into SL. The problem has been ongoing almost a year and the Lindens have turned a back on the issue and getting support from them on this is null and void. Feel free to start using the expession, "...as useless as a Linden Support Ticket."
That out of my system, I'm here to report one cure that, for me, has gotten me in world reliably with this card. Because search as I might over the last 3 weeks, I found no answers to cure this issue:
With this card, make sure you have the latest drivers from ATI, currently CCC 8.12 build.
I'm running XP just for the info.
No Linden browser will work with this card, and the Linden software is the only issue I've found with the card, so shame on them for not doing something about this problem.
Download the OnRez browser for SecondLife: http://viewer.onrez.com/
Install per instructions, at the first screen go to preferences and hit the graphics tab. For a fail safe, turn off both the "Basic Shader" and the "Atmospheric Shader." Apply > OK > start the viewer.
This method has me rock solid inworld. I have turned on the "Basic Shader" and still remain rock solid. I know if I hit the "Atmospheric Shader" the crashes will return, as initially I had both these on trying the OnRez browser. Even with both shaders on, I lasted much longer in world then any Linden browser ever allowed. So if you feel daring you might try both shaders. Perhaps your setup and this browser will allow success.
Good luck with it. You'll need it.