Be sure you have the correct power supply. Lacie made a bunch of drives with that four pin connector, but they came with many different power supplies, and using the wrong one could hurt the enclosure.
If you're not getting power to the drive in the enclosure, try removing the drive itself and installing it in a desktop computer to determine if the problem is with the drive or the enclosure. Frequently the enclosure is the problem, which still means you can use the drive as an internal without the enclosure.