That looks like a physical problem with the drive (or the USB cable you are using to connect the drive). Definitely try connecting using a different USB cable and if that doesn't work contact LaCie, they're usually pretty good about getting issues like failed drive ports resolved.
(Also, good for you for backing up!! )
Using the same cable or have you tried a different cable? Is the drive directly connected to the USB port and not going through a HUB?
If you've tried different cables on two different machines not through a HUB then yes I'd say the USB port on the drive is no good.
USB should be plug & play, no need for you to do anything to get the system to see it.