You've an iMac G5, I think, and a Sony HC3 and a Canon camera.
[..It'd be handy if you go to the "My Settings" item in the column just to the right of this message (..you may need to scroll up first to see it..) and add those specs to your User Profile; then we'll all know exactly what equipment you have..]
Canons by the way, don't like to have anything else on the FireWire circuit (..e.g; an external hard drive..) while they're attached to the computer; so if you're having Canon problems, too, and you have an external drive, Eject that drive first before attaching the Canon. Sony camcorders don't care.
You said "..I can't imagine they didn't stick at least a stinkin' cable in the box for an expensive camcorder like this one.." ..that's probably because PCs tend to have a 4-pin FW connection, whereas Macs use a 6-pin connector on the computer, so Sony would have had to put TWO FW cables in the box along with the camcorder: instead, they let you choose the cable which you want.
You said "..my suspicion is, in HiDef mode, it's too new a camcorder to be recognized.." ..no: it conforms to the same HDV specification as Sony's earlier FX1, Z1, HC1, etc, so it should be recognised by your Mac.
I don't have the exact same model as you, but your HC3 menus are probably pretty much like the HC1 and FX1 menus, so here are some suggestions:
1 - In iMovie HD 6, go to Preferences, and, under 'General', set 'New Project frame rate:' to '25 fps' if you're in Europe (..your 'My Settings' details don't show where you are..) or to '29.97 fps' if you're in the USA or other NTSC country.
2 - Set the camera to Playback mode, and in the sub-menu "VCR HDV/DV", set the choice to 'HDV' or 'DV', depending on what you've shot. Don't leave it set to 'Auto'. Notice that the menu says "Unplug i.LINK to change", so if the camera's already plugged into your iMac, unplug it, and then reconnect it later.
3 - In the sub-menu called "i.LINK CONV", make sure that it's set to 'OFF'.
4 - In the "DISP OUT" sub-menu, choose 'LCD PANEL'.
5 - Shut down your iMac, disconnect all items such as mouse, keyboard and any other accessories, disconnect it from the mains electricity supply, and leave it to stand for 15 minutes: Lennart suggests this as a way to reset your FireWire ports. After 15 mins ..or 20.. plug in the mains again and restart your iMac. Don't have anything connected to it except your mouse & keyboard.
6 - Put a tape in your HC3 (..HDV if that's what you want to import, and it matches the choice you set in -2- above..) and touch Play. Plug the FireWire lead between the camera and your iMac. Start iMovie HD 6, choose 'File' and 'New' and click the little triangle next to "Video format"..
..so that it points
down and then choose the appropriate type of project: for a Sony HDV tape it's 'HDV 1080i'. ("HDV 720p" is for JVC camcorders.)
(..note that 'Where' should say 'Movies', not 'Pictures' as in the pic above..)
7 - When your new project opens, slide the little onscreen selector from the "scissors" icon to the "camcorder" icon, and then click on the camcorder icon itself to choose the name of your camcorder, if it's there. It may show "DV-VCR if it doesn't show the exact name of your camcorder. If no name is showing, and the iMovie screen says "No Camera Connected", quit from iMovie and then restart iMovie.
I usually suggest - if none of that works - to "kick start" iMovie by playing back a bit of footage that's already in your project ..but if you can't import any, then you can't do that ..
EXCEPT that I'm now going to upload some HDV footage to my .Mac page, so that anyone can download a "starter" clip to drop into a project (..but it'll be PAL [HDV 1080i/50] not NTSC [HDV 1080i/60], sorry..)
Anyway; those items above, 1 - 7, always work for me ..every time.
If you try all those, in that order, and it still won't import, then (a) try a different FireWire cable; (b) try a different Mac; (c) check the date and time in your camcorder: if they're set to a date or time
earlier than today's date and time, as it's just possible that the Mac might not import from the camera if the date is prior to today; (d) someone else suggested pressing the 'Reset' button (..probably with a paper-clip..) on your camera ..that's probably visible when you open the fold-out monitor. I've never done that to any of mine, and it might wipe out the existing date and time, but it may be worth a try. If you do that, quit from iMovie and restart it, as changes made to the camcorder's settings
while it's connected to iMovie may not be recognised by iMovie.
NOTE: The date and time
MUST be set in any camcorder which is to be used with iMovie
before you start shooting, as - if they're not - then there's no 'timestamp' recorded when you shoot, and iMovie can't see any difference between the clips, and will import everything as one long clip instead of importing your shots as individual clips.
..I hope that at least some of that helps..