Arch linux system requirements
What You Will Need
* A working knowledge of Linux and your system, esp. your hardware
* Arch Linux installation media (see the mirror list)
o Either the Arch Linux Install CD, or
o 2-7 floppy disks, depending on what you need: SCSI, ethernet, etc.
* Either an i686-based computer (PPro, Pentium 2 or higher, Athlon/Duron, VIA-C7, etc. Note that AMD K6, Transmeta Crusoe, CyrixIII, and VIA-C3 are NOT supported.), or
* An x86-64-based computer (Pentium 4/Celeron with x64 support, Athlon x64, Core2)
* Some time to kill
You could probably do a minimum install of Arch linux on one of those machines, but for all my experience, I have yet to have problems installing Slackware on older machines. Depending on your memory capacity and video card constraints, you might not be able to run a window manager, but the OS would be there and functional.
I've heard Vector Linux is fairly lightweight and works pretty well on older hardware, but I've not had any personal experience with that distro other than a quick install and test of it.
I say try Xubuntu or DamnSmallLinux. I know DSL would work well (the entire image is under 50mb) and I use Xubuntu on a similar system, although this one has 192mb ram. Xubuntu would probably be too heavy, but DSL or Puppydog Linux might work alright. I don't know anything about Arch Linux, so i can't really help you there, but from my experience, DSL would probably be the best route. It even worked ok on a LiveCD.