May I also recommend Alpine Linux
in your case? When I decided to revive an old 800 MHz pc (unfortunately not an Intel or AMD but a VIA one!) I ran into trouble as well. I couldn't get Arch or Gentoo started, Lubuntu didn't even display the language selection...
Thanks to Alpine that pc is now working fine again (except for Xorg; however that is not the distros fault but a problem with the problematic graphics chip).
Compared to the mentioned AntiX it's extremely frugal when it comes to ressource usage. You don't need several GB of disk space - much less is needed for a base install. And it could also be interesting for you since it can run a full-blown desktop (Xfce!) with about 40 (!) MB of RAM - honestly. You could actually work with a real desktop environment on a 64 MB system (if you don't consider firefox and tabbed browing a must!
In general this OS is meant for embedded systems and such but it can also be used as a desktop system. I especially found package management very pleasant and in general it works fine for me without any unnecessary bloat. Thanks to many scripts it's also nice to work with.
Of course there are a few downsides of it. The biggest one probably the fact that there are not too many packages available. If KDE or any Qt applications is a must for you, you're lost. Also building your own packages (with an excellent building system!) can in certain cases be problematic due to the fact that it's not build against the standard glibc but the tiny µclibc library.
If you can live with that, all should be well. Also if you just want to find anything that might be able to ressurrect your box, this distro could do the trick.
Whatever you choose in the end: Please post once more here what distro you got working. I'm interested in Linux on old pcs in general and would like to hear of your experiment again.