As long as your other machine has a serial or parallel port, you can use that for networking. For serial it's a null modem cable, for parallel a laplink one. You'd use PPP, and it'd behave like a two machines connected directly via crossover ethernet.
You can even share the connection of the other machine, and get internet on the older one via this.
Infrared would be similar, but for transferring files it would be easier, as long as your phone has IR too.