See if you can access the HDD doing the following. You can use either a DVD or Rufus with a USB flash drive. You first need to disable SecureBoot in UEFI settings. Also disable Quickboot/Fastboot.
Download Mint Cinnamon. Burn the iso to a DVD by right clicking and selecting Burn Disk Image. For the USB download Rufus. Run the program with the USB flash drive attached. Select GPT partition scheme in the dropdown box. Leave all boxes as checked. Where you see FreeDos in the dropdown box select iso image. Click the small icon and browse to the Mint Cinnamon iso you downloaded. Press Start. All data will be wiped on the flash drive so backup and info it has.
Attach the USB flash drive or use the DVD. Boot the computer and start tapping F8 which will bring up a boot menu. Select the USB flash drive or the DVD drive in the list. Mint will boot and it will look like it's asking for some input. Do not enter anything and wait until you are at the Mint desktop. Once at the desktop click the Computer icon. Your HDD will be in the lower left pane marked as GBs. If Mint can mount the disk then you will see a File Manager window open. Attach a USB external hard drive. A USB icon will appear on the desktop and another file manager will open. You can copy and paste between your internal and external drives.
Hopefully Mint will boot. If not then I think you are looking at some type of hardware problem.
Was the computer pre-installed with Windows 8 or was it 8.1? The key is embedded in firmware so a clean install will autoactivate.