Hi,
Best is the NIC route plus cross over cable and network the machines.
Cheapest is to put the old hard drive in the new machine permanently or even just temporarily.
Simplest is a USB to USB laplink cable, plug and play, the old machine is Win 98 or above so this will work provided it has USB ports. Not fast but it does work.
Most complicated is the parallel / serial laplink cable route
Alternatives
Put the hard disk from the old machine is external USB or Firewire enclosure
Use USB 2 to IDE adapter to connect old hard drive to USB port on new machine without opening new machine.
hth
Ceri