Is the camera outputting a picture to your TV via the A/V out? If so two things to check on your PC.
The driver needs to be 1394 (legacy) before the PC will recognise the camera.
I had a problem with the 1394 cable plugs being just too short for my Canon HV20 camera. Replaced the 1394 cable with another make and this sorted the problem.
I am trying to find the operating manual for the Sony HDV 1080i camcorder model no. HVR - A1J. I have the 4 pin to usb firewire cable but my computer is not reading it. I am trying to transfer video footage from a mini cassette to a computer.