According this Ogre manual
from 2006 ATI doesn't support vertex fetch in their cards (Radeon X1n00). nVidia do support it in both their 6600 and above range. ATI support an alternative called 'Render to Vertex Buffer', but this is not standardized(in 2006) and is very much different in its implementation, so cannot be considered to be a drop-in replacement. This is the case even though the Radeon X1n00 cards claim to support shader model 3 (which requires vertex texture fetch).
And according Vertex and Fragment Programs Manual
hardware support for vertex texture fetching is not ubiquitous and says to use the uses_vertex_texture_fetch directive when declaring vertex programs that use vertex textures, so that if the client hardware does not support it, technique fallback can be enabled, as described in manual.
It is not required to use this attribute for DirectX-targeted shaders, since vertex texture fetching is only supported in OpenGL shader model 3 and above, and can state this as a required syntax in the shader definition.
So the question is: If it is still true that current ATI drivers and newest graphics says that it support shader model 3 and in fact it doesn't is not FreeOrion fault that FreeOrion doesn't run on ATI cards. But maybe switching to fragment directive via using above directive for vertex texture fetching is solution to this problem. Another solution is to try open source ATI drivers.
I can't test this because I don't have ATI.
And another question is if nvidia-cg-toolkit is required on ATI or there is some alternative.