check whether it is spinning up - it may just be the power supply! My Lacie drive did the same and it turned out to be the power supply unit, I replaced that cheaply and all was fine. it may look like the power supply is working as mine did but the power it was supllying was varying so a new one was needed.
"I have an older Lacie FW 400 external drive that will not mount. I opened Disk Utility and it does not show up there either. Does anyone have any advice for how I can regain access to it?"
As the poster above mentioned, it -might- be the power supply. For some reason, LaCie has a high failure rate with their power supplies.
If the drive is out-of-warranty, and you don't mind opening the enclosure, you might do this (it will cost you about $25, however):
1. Get one of these: http://www.amazon.com/s/ref=nb_sb_noss?url=search-alias=aps&field-keywords=usb+sata+dock&x=0&y=0
(many items shown, they all work the same, pick one you like that's cheap, USB3 would be a plus)
2. Open the LaCie enclosure, take the drive out of the case
3. Connect the USB/SATA dock to the Mac, put the drive into it, see if it mounts that way.
The above "solution" works only if the drive itself is a "SATA" (serial ATA) type drive. If it is an older "IDE"/"ATA" type drive, it won't work with the dock. There are "dongles" you can buy that will do the same thing, allow you to connect the drive via USB. But if the drive is SATA, the USB/SATA dock is a VERY handy device to have around, for situations just like this one.