I find it hilarious that others are actually suggesting things like "do a refresh, it's Windows 8", or "Just use a keyfinder.".
Read the question the OP posted. The drive is CRASHED. Worst case scenario, it cannot even be read by another machine directly connected to SATA.
"Hey don't worry, just use the recovery disks!" - What is this, 2003? Most vendors (if not ALL by now) just shove your "restore disk" onto a separate partition on the hard drive [which, oh yeah, is dead now].
So, you can't use keyfinders cause the drive is toast, can't use recovery media because we've moved onto this streamlined 'it's on your hard drive' era, and a refresh is completely out of the question cause we obviously can't boot into Windows.
THE ACTUAL SOLUTION:
Get your hands on some clean installation media. If an official vendor will not give it to you, torrent it. We merely need to get Windows installed onto the machine with the NEW drive you have. The BIOS will at least tell us which version of Windows 8 it is. (If not, assume non-pro for consumer, and pro for business).
Click "skip" when the installer asks for the installation key when prompted. On the next screen, you'll hit CTRL + SHIFT + F3 to get to the "I'm an Admin, let me set up this computer for first time use" mode.
Download RWeverything (this reads the key out of the BIOS on Win8 Machines -- see this thread on how to use it) http://rweverything.com/download/ Then, hit the start button and open up Windows Activation (not the Win8 tile app, there should be a different one that shoots you back to the desktop). It will have an "activate" button. Click it and let it fail activation the first time. Then, it will ask if you want to try with a new key.
Insert key you found with RWeverything. Activate. SUCCESS.