I am using a LaCie Rugged, and when I plug it into my Mac, a message pops up saying, "DISK INSERTION: The disk you inserted was not readable by this computer." Buttons read, "Initialize," "Ignore," and "Eject." It does not show up in my Finder or on my Desktop. Please help! Thank you so much!.

You have a double crash. You will need your OS reloaded.

Unfortunately, that does not sound good. What format is your drive? (Mac OS extended/ FAT32/ NTFS/ etc). If it is a mac format you could try something like drive genius to hopefully be able to get it working again. If it is a different format you could try G-parted or there are a lot of good tools on ultimate boot cd (although they are kind of geeky and hard to use).
http://www.ultimatebootcd.com/
Unfortunately if it is starting to die, and the info on it is really valuable to you, your only option may be able to send it off to a data recovery place, but they are VERY expensive (sometimes $1000+ and it's not even guaranteed to work). I wish I had better news.
If this was a help please give me 4 thumbs up as I am trying to build up my rep on this site!

First, connect the hard drive to the computer. Go to the search bar in the top right and search: Disk Utility. Then select your hard drive (not a subsection, the actual hard drive). go to the First Aid tab, and click "repair disk".

If this does not fix it, then I am afraid that your drive is dead.You may have abused the product in some way (dropped it, dropped it while it was on, bumped it, didn't drag the drive to the trash can, etc).

Are you connecting it to the Windows now? If yes, Click on START > Run - type diskmgmt.msc
You will see your drive listed here
Right click and click on format (do not proceed if you need data on the drive)

Once done, you should be able to use it.

Hello,
if the option is available in disk utility, run First Aid.
Second option will be to run a third party partition repair utility if you have one available. If it does not fix the issue, go for a data recovery software. Some have a free trial that allows you to verify if the data on your drive is retrievable with their software before you buy the complete version to recover the data.
If the software does not do it, you can try connecting the hard drive inside the enclosure directly to the computer, but take note that:
-Taking the drive out of the enclosure will void the warranty
-If any electrical damage is present on the hard drive, it can damage your computer, so unless you are competent with electronics and can recognize healthy components, do not connect the drive to a computer.

If all those have failed, you will have to contact a data recovery center for a complete diagnostic.

Make sure that you do not format or initialize the drive.
If your data is ever available during the process, copy it to two other devices/computers to prevent the risk of losing them again.
Regards,

Try a different "data" cable between your computer and the external disk-drive.

Try connecting the unit to a different computer.
If it fails there, then the unit itself has a problem:
Either:
* the USB-to-disk-drive adapter (inside the casing) has failed;
* the disk-drive (inside the casing) has failed.

Disassemble the external unit, and remove the disk-drive. Connect it as a "slave" disk-drive in some Apple Computer, to see if the data on the disk-drive can still be accessed.

Check with LACIE, to see if their "warranty" is still valid, or if it has expired.

The Disk inserted dose not work

go to applications, utility folder, disk utility
then format the drive in any other way besides
dos.

You need to upgrade the H4  firmware from Zoom website
http://www.zoom.co.jp/english/download/software/h4.php

You will need an external SD card reader.
Good Luck

Mount.... sound like you got a Mac... Don't use the Mac sugested fix. The lacie Website has many revovery software options and Third party software is very good at that as well

I would try that first or try to contact a lacie tech and/or a mac tech.

If this is helpful please email and notify fixya. Thanks