Alhamdulillaah, through some diligent searching and more than a few unnecessary steps, I was able to get my not-bottom-of-the-line ATi Radeon x1600 AGP video card working reasonably well on Fedora Core 6. Sadly, this series of discoveries happened after I had decided to resort to a complete wipe/reinstallation. However, the decision to hose the old system was also influenced by the fact that I wanted to try out a new filesystem – ReiserFS in this case.
The key breakthrough was a discovered on the Livna wiki that seemingly should have more prominence than to be accidentally discovered by searching “fglrx” on their site. Nonetheless, by adding the lines
Section "Extensions" Option "Composite" "Disable" EndSection
to my xorg.conf file and restarting X, I was able to overcome a problem caused, at least indirectly, by the driver’s assumption about AIGLX – which is something else that I might be interested to look into later. Now I had 2D acceleration. But I was still not getting what I wanted from fglrxinfo (i.e., no error messages), and it was complaining about DRI and whatnot, so a search for the error message I was getting directed me to the wonderful folks that are working on DRI and their troubleshooting page. By adding the following lines
Section "DRI" Mode 0666 EndSection
and restarting X, I was finally in the bountiful land of accelerated 2D AND 3D! Alhamdulillaah!
(2006-12-09 Edit): I discovered, after trying my own fix on a second installation of FC6, that WordPress so kindly converted my double-quotes to “curly” quotes, which the aticonfig utility so kindly informed me was invalid for an xorg.conf config file. I’ve (hopefully) corrected it above.