Having a similar problem with the La Cie 500gb. Powerbook G4.
The problem that has been inherent with all LaCie external harddrives, is the interface in the case itself.
All external harddrives have a Style of harddrive that is used in a laptop, or one that is used in a desktop computer.
Laptop harddrives are 2-1/2 inches across in width.
Desktops are 3-1/2 inches across.
Your LaCie will have a 3.5, (3-1/2) inch desktop style harddrive, inside the case.
There are two main Types of harddrives.
IDE and SATA. (There is also a newcomer. SSD. SSD isn't being used in LaCie external harddrives at the moment, to my knowledge)
Your LaCie will use a SATA harddrive inside it.
This is an example of an average SATA harddrive,
The photo of this harddrive is tilted at an angle, that doesn't readily show the interface connection, but it helps to explain.
At the bottom of this harddrive in the photo, and to the left, is the interface area.
Viewing the harddrive, look at the four metal pins on the extreme right of the harddrive. To the left of these pins is the Jumper pin area. (Has a white jumper on two of those pins)
To the left of the Jumper area is an opening, and to the left of that, is a long slot. The first small slot area is for the 7-pin Interface cable.
(Data cable) The next slot to the left, is for the 15-pin power cable.
This 7-pin Interface mates up to socket holes in a connector, of the case of the LaCie external harddrive.
It is this interface connector, inside the LaCie external harddrive case, that is the problem.
Buy a quality, in-expensive External Enclosure, take the harddrive out of the LaCie, and install it in this enclosure.
Examples of 3.5 Sata External Enclosures,
(From $15 to $35, is a good range for a decent external enclosure)