I had the same thing happen with my first copy of the 1DX. I heard something that sounded like the shutter locking up, and then the camera was dead. None of the buttons worked, couldn't bring up the menu, etc.
Turning off and back on solved it for me.
After wrestling with what to do, I eventually returned that copy (I was lucky, it happened within the first 30 days); the replacement hasn't shown the issue. Though, to be fair, it has far less actuations than the other one did when it locked up (happened around 2,200 photos).
I didn't get an error code on the screen, and I looked through the error log on the camera, and it didn't seem to know that this had happened. Could just be a hard crash.
What BIOS version are you using? Mine happened with the BIOS that originally shipped.
Wish you lots of luck :/