Steps used:
1. Boot the machine using the DSL liveCD (use what ever method you use to boot live distro's: USB, floppy, CD, etc.)
2. Downloaded Processing 1.5 to the desktop.
3. Double click the downloaded file, DSL will launch a utility to extract the contents of the file and let you select where you would like it extracted to.
4. Now use Processing like normal.
This was just a test to determine if DSL had enough base support to run Processing 1.5 without any additional downloads (it actually ran it pretty smooth with the above hardware, everything was happy just living in RAM).
If one was to make this a permanent platform, then you would want to add a hard drive and install DSL on it.
I have NOT tested standalone Processing programs with this setup(only running in the Processing environment), but to do so should only require a java installation that is compatible with DSL and Processing 1.5.
The niftyness behind this is that you can create a standalone custom controllers, using hardware acquired for pennies if not free.
Hopes this provides some encouragement to recycle older machines that would have otherwise been on their way to the scrap heap!