I just bought the same thing.
If you disconnect, then re-connect the A/V Link to your firewire port does your computer recognize a device was just connected? If you are using Win XP you should hear a sound when it connects.
If not, you might try another firewire device such as a Digital Camcorder or external hard drive to see if the firewire port is working.
I have another question...
I am able to preview and capture video using the composite or S-video input ports, but I do not get any video when I try using the Component input. Have you tried using Component input when it was working?
You can also try the power button on the rear. Mine hangs often with the older software and i have to "bump" it. Look in the Windows device manager and it should have a device entry for Imaging Devices under that should be something like AVC Compliant DV CamCorder. If that is not there, run "scan for hardware changes" by right clicking on the top "ComputerName" of the devicde tree.