3-4 old computers = general purpose cluster?

You can certainly do this. Any linux distribution should be able to do this out of the box.

X11 was designed to allow programs to be run over the network. X11 has the concept of a server, which is running on the computer that you are sitting in front of. You can start X11 clients on any computer, and they will display on the X11 server. X11 uses quite a bit of network bandwidth, but 100 MB should be fine.

With this setup, you will be running individual programs on different computers. Generally, when people talk about clusters they mean applications running across several machines. There are very few apps out there that are designed to run across multiple machines, outside of scientific number crunching.

Nobody mentioned a Beowulf cluster.