This problem seemed to be random, but now it's constant. Whenever the screen is on, the viewfinder glows red. If I remove ther lens I can see that all the RED LED's in the viefinder are illuminated. Screen off - no LED's. This makes it impossible...
I've had it a year, so it's out of warranty. It's obviously a defect/design flaw. I know 8 people with the 5D MKIII - six of them are now experiencing the same problem!
Almost any HDD data recovery software will also work, even if you formatted the card. The card is just an external drive as far as your computer is concerned.