Ubuntu 16.04 LTS unrecognized hard drive -- not enough disk space to install

Had the same problem with almost the exact same hardware. The issue was with the SATA mode. It needs to be changed to AHCI mode in the BIOS settings. This can be done with the instructions found here, printed below for completeness.

  1. Run Command Prompt as Admin
  2. Invoke a Safe Mode boot with the command: bcdedit /set {current} safeboot minimal
  3. Restart the PC and enter your BIOS during bootup.
  4. Change from IDE to AHCI mode then Save & Exit.
  5. Windows 10 will launch in Safe Mode.
  6. Right click the Window icon and select to run the Command Prompt in Admin mode from among the various options.
  7. Cancel Safe Mode booting with the command: bcdedit /deletevalue {current} safeboot
  8. Restart your PC once more and this time it will boot up normally but with AHCI mode activated.
  9. Bask in the reflected glory of being a total Windows 10 God

You can then boot in to Ubuntu from the USB, and the installer should recognise the hard drive.