It's unlikely that the cable you've got is the right one. If your cable is just a bit of wire with two plugs on the end and no electronics then it's definately not what you think it is. The serial port is -/+12V whilst the parallel port is 5V and would require some electronics somewhere in the middle to convert between the two.

You basically need to get a null modem cable to connect between the two machines or a laplink parallel cable.