Support is planned OpenCL 1.0 in Cycles? I have an AMD graphics card (HD 5830), but the rendering runs on the CPU, because Blender not see my graphics card. I think that it will render faster on the GPU than the CPU.

UPD:

I waited the final release version of Blender 2.75 and is now sees at once my GPU, but Cycles Render will not start. The message "Loading render kernels (may take a few minutes the first time)" and then appears "OpenCL build failed: errors in console", in a console Error E013: Insufficient Private Resources OpenCl

On my computer, little RAM, 3GB. Device Manager shows that at the time compilation uses all available memory. Maybe 3GB not enough to successfully compile?

Someone you know, there are cases of successful run in cycles of rendering graphics that do not support AMD GCN?

P.S. Maybe in my case worth trying to start already compiled kernel OpenCL?
Not all ATI cards are supported. 

The list of supported cards per Blender Development can be found here. While this is not the entire list of cards that have shown to work, I believe they are the GPUs that have been tested "working" by development. From what I've observed from other ATI users, any card that does not have OpenCL 1.2 or 2.0 support, does not work with Blender 2.75 (and 2.74 w/ ATI Patch), and will not show in the list of Computing Devices.

With that said, Blender only works with the latest drivers from AMD, and if that driver does not have the OpenCL support for older cards, Blender will not support it. On a good note, the Blender viewport will support more versions of OpenGL in the future. Some users have had luck using beta drivers with older cards, and using an ATI patched Blender (2.74.5 - 2.75rc2).