OK, so have you got The ATI proprietary drivers from ATI, or are you using the ones that came with Slackware -- basically, have you got 3D acceleration/rendering? This might me as simple as configuring the xorg.conf file (which maybe you should post, as well as any other information from near where the error occurs, so we can see what's going on when it happens). In a console, what do you get if you type
glxinfo | grep direct ? It should say something like
'Direct Rendering: Yes'..
So, have you been able to run other software/games similar to Doom3 graphics-wise? Or is this the only thing like it that you have tried -- what I'm asking is if this problem is 'Doom-specific' or if maybe it affects other programs too.
You might search the web for other forums too, like ones that Specifically cater to games like Quake, Doom, WoW on Linux; Also if there are support forums on the ATI site; I don't play games so I haven't got a link handy for you, but I have seen the forums on the net - they're there somewhere

I hope this atleast gets you started in the right direction. Also, Search LQ (if you haven't) for terms or tags like 'Doom' 'doom3' 'ATI and doom3' 'Doom3 and Radeon' and see what other users may have experienced like this.