Swapping out power supplies also worked for one of my customers....

May be worth trying a spare. The same power supply is used on other Lacie equipment, such as their dvd burners.

I should have also mentioned that both firewire (1394) and usb interface boards for lacie and other equipment is static-sensitive. If one touches the firewire or usb port or plugs in a cord (either to the Lacie drive or the port on the Mac), there's a chance that the interface chip will be zapped. On the desktop Mac, one can install another PCI firewire/usb card, but on the external drive not under warranty, you'll need to pull the drive and place it in another case. One that is under warranty may mean that you have to void the warranty to get at your data. Normally, the drive itself is fine -- just the interface board is toast.