Most of these things are a matrix of some kind, so driving them is a bit more complex than just using e.g. an LED-Wiz. Look up those chips running along the length of the LED assembly itself. They're probably shift registers or something of the like. If you trace everything back out to the connector between the LED board and the "CPU board" (for lack of a better term), it's probably a fairly simple interface. You can then just drive that with a small micro or maybe even your parallel port.
If you have something to hook it up to, you may be able to reverse engineer the protocol use by its serial port (or however it hooked up for programming), but that'll be tough without the programming software.