It sounds like your backup is incomplete or damaged. See if you can download macOS 10.11 El Capitan to see if you can install it so you get a good version of macOS. I'm suggesting 10.11 since it can be downloaded outside of the App Store.
Use this Apple article to download and install the macOS 10.11 El Capitan installer:
https://support.apple.com/kb/HT206886
Then create a bootable macOS USB installer using instructions found in this Apple article:
https://support.apple.com/en-us/HT201372
When you boot from the USB installer make sure to use Disk Utility to select the physical drive and erase it as GUID partition and MacOS Extended (Journaled). If the physical drive is not seen in the left pane of Disk Utility then click on "View" and select "Show All Devices". See this Apple article with details on how to erase the physical drive:
https://support.apple.com/en-us/HT208496
Once you perform a clean install of 10.11 you can try migrating your user account data. Don't migrate anything else as it may be incomplete or corrupt.