Well, my conclusion is, because you cannot start up in any of these modes, that, yes, you have a failed HardDrive.
I would look back at Lisa's post and look at getting another HD
I would recommend if the rest of the computer is running good look into getting a new SSD from
OWC or
Crucial.
Lisa
All you will need to do then, is to install the OS X Yosemite on it, and restore from the backup.
EDIT: Personally, I would keep trying the restart holding ⌥ALT Key until you see a list of Drives/Partitions come up, until you receive a new HD. I have, in the past, had to restart about 10times at one stage for the ⌥ALT holding activated and showed all my drives. . . . You
might get lucky, 1 time, where you can then go into the Recovery Partition, and repair the drive.
If your Backup, is a Bootable Backup from CCC or SuperDuper, boot into that backup, and then go into Disk Utility and repair the Mac HD from there.
If its a TimeMachine Backup, you won't be able too.
EDIT 2: You are still going to have to get a USB Stick with the OS Yosemite soon it, to install on a clean HD, and this is why I said to persist with trying to boot into the ⌥ALT mode to repair the HD so you can Download the Installer again.