Your camera is not the IEEE 1394 thingy, thats the firewire card. When plugged in and turned on, your camera should show up under imaging devices. You mentioned a 4 pin to 4 pin cable?? thats strange as most OHCI firewire cards use a 6 pin connector. Some proprietary capture cards use 4 pin connectors. What kind of firewire card do you have? It may need drivers. Are there any devices that have yellow exclamation marks in Device Manager??
