It's been a few years since I used one, but the last time I used it successfully, I used the front smaller FireWire port and the rear A/V ports (it probably does both features from both sides, but that's how mine worked best for my physical setup). However, I had the AC adapter it shipped with. If I recall, the ADVC lights up bright blue underneath the button when on, with or without analog A/V connected.
The mini port does not draw power from the FireWire bus, though, so if you're using that one, go for the larger 6-pin one instead, which should power it. Hopefully that's the issue!