adamk75,

I was able to reinstall Mesa just now.

This first pastebin is the output for glxinfo, which tells me I have direct rendering.

This pastebin is the output for 'LIBGL_DEBUG=verbose LIBGL_DRIVERS_DIR=/usr/lib64/xorg/modules/dri/ glxinfo'. What caught my eye here are the following lines:
Despite erroneous as it is, i got around 930FPS on glxgears with the radeon driver.

So, thank you very much for the assist so far!

Alright, so you have 3D acceleration going. You won't be playing doom3 with that setup, but KDE compositing and various light games should work. The message about a missing drirc just means you don't have a configuration file setup which can be used to set various values for the driver. You can create such a file with driconf (which does not come with Slackware and, iirc, does not exist as a slackbuild), but it's not necessary. The driver will just use defaults.

The IRQ message simply means that you are either using a kernel too old to support IRQs on that hardware or you are missing a specific firmware file necessary for IRQ support. Without IRQ support you can't sync-to-vblank on HD cards. That is really the only downside.

Mind you, newer versions of the Mesa driver would actually give you opengl 2.0 support and even let you play doom3 with improved performance (though still not as good as fglrx, of course).

LAST UPDATE:

After recompiling kernel with fore mentioned options, I've restarted and all is worknig rather fine ...

Lucifer4o,

please summarize what kernel changes you made and what driver you're using.

I've copied config-huge-smp-2.6.33-smp.

Changed only:
CONFIG_PREEMPT=y
CONFIG_HIGHMEM64G=y
CONFIG_MPENTIUMM=y

recompiled and seted radeonHD driver.

My card is ATI RADEON HD3450. And all is good for now ...