A couple of things:
1. What exact Mac OS are you currently using?
2. For the external drive, which "cloning" software did you use, SuperDuper! or Carbon Copy Cloner?
3. When you made that bootable backup, what Mac OS was on the machine at that time?
As you might know, after rebooting your machine from that bootable external drive, you can use Disk Utility there to Verify and Repair the internal drive on your Mac. But, it seems to be a software issue. So, after you download and save the applicable "Install macOS Whatever" file from the App Store (you can do that via your bootable backup), use Disk Utility to Erase and Format your internal drive, then launch that "Install macOS Whatever" file you just downloaded, perform a fresh, clean, "virgin" installation of that Mac OS, and then, via Migration Assistant (you'll be offered to do this), "migrate"/copy needed "stuff from your backup.
Of course, you'll lose any recent "things" you have done from your Mac. Maybe you could try and save as much of that recent stuff as you can to the backup. Myself, I would do that with my Quicken Account file, any software updates that I downloaded, etc.
Also, are you positive that all your third party apps are compatible with the OS you are using on your Mac (and what you were using when the backup was made)?