Yes the computer will drive a GAZ scoreboard but you will need a computer or laptop with at least 2 serial ports. You can easily add an additional port by using an inexpensive USB to serial converter; but my preference is to add a pcmcia slot card for the additional serial connection. Check elsewhere on the forum for specific brands/models and that they will work with your flavor operating systems.
As for the cable, it is a simple 9pin to banana, not quite sure of the pin out but it is the normal pins for transmit and ground.