A: do you hear the HD platter spin up at all?
B: do you have a power indicator on the HD enclosure?
LaCie doesnt make HD, its a Seagate 3.5" inside that box. If it does NOT spin up at all, then you likely have a bad power supply to same via the SATA bridge (deja vu here).
LIkely your HD is fine, and only the connecting interface is bad and you can put the internal HD in the case in a HD dock to get data.
report back on A and B.