I, too, have this problem, only with a Sony DCR-HC32. Relevant versions: OS X 10.4.4, Final Cut HD 5.0.2, Quicktime 7.0.4. Yes, I most definitely am using a Firewire cable that I went out and purchased, not a USB cable.
Things tried that did not work:
1) Switching the dock to "off" (as this switch controls the USB port)
2) Switching between FW ports on my G4
3) Trashing the iMovie plist
4) Resetting PRAM
5) The "Garageband trick"
6) Trying all of the above on a fresh admin account
7) Repairing permissions
The first time I logged into the fresh account iChat was able to see the camera, and it even displayed live when I launched iMovie with the camera in record/tape mode. However, once I switched it to Play/Edit then it reverted to the status quo of having the blue screen instantly pop up with "Camera connected" yet no video imported or viewable on the Mac (even though the camera was being controlled properly).
Like the original poster I don't think this is an acceptable situation, and I am going to return the whole camcorder setup as soon as I am able to.