LaCie makes network drives, USB drives, fibre-attached RAID arrays; what have you got? The model might help us figure out what a blinking blue light means, too.
Assuming it's a USB drive, there are several standard tests that just involve changing one thing at a time:
- Change the USB cable
- Try a USB pen drive in the computer's USB port to make sure that it's working
- Try the LaCie drive on another computer to see if it works there.
- Look at the drive in the Disk Manager to see if it's recognized, if the partitions got messed up, and so forth.
- In extreme cases, and assuming that the case comes apart, and if you want to take the risk, you can open the case, take out the drive, and attach it directly to the motherboard.
If none of the simple tests finds the data, we might switch over to using some drive imaging tool like Clonezilla to recover as much of the data as possible. I'm hoping that it will be something simple like a bad USB cable, a dead port on the computer, or power. For example, does your drive plug in to wall power or draw all its power off the USB connector (again, I assumed USB for a start). Some drives draw almost all the power that a USB port will supply, and even a little degradation could push it over the limit.