Best way to get data off a computer with no support for USB or Ethernet?

To be honest, taking the drive out would take about 30 seconds, it's probably the easiest way.

Go buy some CDs at the local supermarket or computer store!

download Ubuntu Linux CD or USB, boot from there and it will support USB

using serial port will take forever (depend on the data volume)

there are also DB25 Male / DB25 Male 15C Parallel Data Transfer Cable (norton commander or Windows 'Direct Cable Connection.")

boot Linux from floppy - but it is not GUI :)

DVD - KNOPPIX this GUI is very lightweith no problems even with 128MB

you also can do a backup of user's data if HDD dies (it is about a time)