If you happen to have a thunderbolt cable and a spare mac you can try your luck with target disk mode. Target Disk Mode is a feature that allows a Mac to act as an external hard drive.
- Connect the two computers with a FireWire or Thunderbolt cable.
Start up the computer to be used as a disk in target disk mode:
- If the computer is off, start it up while holding down the T key.
- If the computer is on, choose Apple menu > System Preferences, click Startup Disk, and then click Target Disk Mode.
When the computer has started up, a disk icon appears on the desktop of the other computer.
Transfer files by dragging them to and from the disk.
Eject the disk by dragging its icon to the Trash. While you drag, the Trash icon changes to an Eject icon.
On the computer you used as a disk, push the power button to shut it down, and then disconnect the cable.
Instructions thankfully provided by Apple's KB
http://www.apple.com/support/macbookpro-videoissues/
Apple has issued a Repair Extension Program for Video Issues. I was experiencing the same problem and had tired several solutions that worked for a short period of time, but ultimately I was unable to get my MBP up and running last night and brought it into an Apple store. They determined that my issues was in fact a video issue and qualified for free service.
If you purchased a MBP between February 2011 and December 2013 and suspect that your MBP is experiencing the same issue, then check out the page URL above to see if your MBP qualifies for service.
Here's an excerpt from the page
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Apple has determined that a small percentage of MacBook Pro systems may exhibit distorted video, no video, or unexpected system restarts. These MacBook Pro systems were sold between February 2011 and December 2013.
Apple or an Apple Authorized Service Provider will repair affected MacBook Pro systems, free of charge. See below for details on affected models and service options.
Symptoms
An affected MacBook Pro may display one or more of the following symptoms:
Distorted or scrambled video on the computer screen No video on the computer screen (or external display) even though the computer is on Computer restarts unexpectedly
Products affected 15-inch and 17-inch MacBook Pro models manufactured in 2011 15-inch MacBook Pro with Retina models manufactured from Mid 2012 to Early 2013
Best Answer
I had a similar issue with my 2018 Mini: I had to delete the .AppleSetupDone file and run the "Welcome to Mac" routine, creating a new admin user there before I could alter SecureBoot, even though the disk had been imaged with an admin user.
Peter Thorn's answer here gets to the exact cause of the problem and provides the solution for a working Mac that has MacOS installed.
If you don't have MacOs installed, you could try booting it in Target Mode from another Mac, which I understand bypasses the Secure Boot! (Though if the drive is encrypted, you'll need the password, unless you're wiping it anyway.)
Alternatively, take it to an Apple Store. The SecureBoot settings can't be changed unless there is a valid admin user, so you can't boot to an external. Recovery is another option, but you say that's not working.
PS. I'd love to work somewhere where you get to keep your laptop when you resign!