The recurring most often than not solution was to put the drive into some other USB or Firewire case. Have you tried that?
I have a Lacie porsche that I bought a couple of years ago and have been using it on my Mac. Recently my Mac crashed and after it was repaired, the Lacie drive was not recognised. I also have a seagate, which appears immediately on the desk top. Would anyone know either how I can reconnect Lacie or back up the data on it?