Yes, you can use a serial or parallel networking
connection but you need an appropriately wired cable (a
cross over cable) often sold as "Laplink" cables. You can
also connect with USB cables but I am unsure how this
achieved in practice.
USB network card may be a solution if you do not want to
open the boxes. But PCI network cards are cheap and easy.
If using Cat5 UTP cable and no hub you need a cross-over
cable.