When you say " went dead " is it spinning up at all ?are you able to see it in " Computer Management " ?
If not the only way you could get data back is to send it off to a professional and see if they can recover anything.
My first instinct would be to rip it out of the case and try to put it in a computer tower, but that's only if you're sure it is a newer hard drive (SATA) and you have a computer with open SATA ports and cables that you can connect it to.
If you can take the drive out of the LaCie enclosure and connect it to a pc you may have some luck seeing the drive from a linux live cd. It all depends on what is wrong with the drive.
Most pc's have IDE and SATA connections these days so you should find a connection to suit.