I just had two LaCie power supplies die on me (it got really hot for a couple of weeks here, and the disks are in the closet, so they died an understandable heat death), which I was able to verify by hooking up different power supplies from other LaCie disks (I have a bunch of them), which had the disk working fine. Upon my diagnosis, LaCie replaced the power supplies, no further questions. The disks themselves never left my house.
The LaCie power supplies spit out two separate voltages - one for the bridge, and one for the disk. It's possible you might just have to get the power supply replaced.
Try to check with a different supply, perhaps at the store.