I'm glad you have a backup!
It sounds like you may have a bad hard drive.
You can try running the Apple Hardware Test although it will not catch all drive failures.
If the laptop has had macOS 10.12.4 installed at some point, then you can try booting into Internet Recovery Mode using Command + Option + R to bypass the local recovery partition on the hard drive.
To check the health of the hard drive you can create a bootable Knoppix Linux USB drive using Etcher (Mac/Windows/Linux). Option Boot the USB drive and select the orange icon labeled "EFI". The computer may appear to be frozen on the Apple boot picker menu while Knoppix is booting so give Knoppix lots of time to finish booting.
When Knoppix boots to the desktop click on the "Start" menu on the lower left corner of the Taskbar and navigate to "System Tools --> GSmartControl". Within the GSmartControl app double-click on the laptop's drive icon to access the drive's health report. Post the complete report here. GSmartControl also has the ability to run the drive's internal selftests. The short selftest takes about two minutes to run while the long/extended selftest can take several hours depending on the size and health of the drive.