Sounds like your OS was somehow damaged during that efi update. Try a command-option-r (hold all three at once) boot to internet recovery. Once in the recovery screen start disk utility and run repair disk on the drive and see if that helps. Tell us what you see when you run the disk repair.
Nothing about that efi update should hurt your OS. It could be you have a drive failure imminent and it just picked this time to go bad.
Disconnect the external display and run off the MacBook when testing this.