** These next two suggestions would not be the first things I'd try** For example, if it's connected with a Firewire cable, unplug the Firewire cable and connect it to your Mac with USB. If you have an external drive that can be connected via Firewire OR USB, try switching from one to the other (only have one cable hooked up at once). I don't know if you mentioned whether the drive is attached to your Mac via Firewire or USB. Tell them DW doesn't recognize the drive. You can also email Alsoft (makers of DW) and ask them for assistance. If you can get it to mount, then run DiskWarrior on it. See if they can help you get it to mount. Next step: Is it still under warranty from LaCie? Call or email them. See if you can get it to mount (show up on the Desktop). Plug it back in after you plug the power back into the drive.
Just checking: Have you unplugged the hard drive, waited 30 seconds, and plugged it back in? At the same time, unplug the USB cable from your Mac.
