You'll want to perform a few diagnostic tests.
1) Remove any non-Canon accessories from the camera. If you are using a 3rd party battery grip (just one example) then please remove it. Also the camera does not actually need a lens in order to power on (it needs a lens to take a focused photograph, but it will power on even if no lens is attached.) So you may also want to remove your lens (and put the dust cap on the front of the camera body.)
2) The camera has a tiny swtich on the battery compartment door as well as on the memory card door. Make sure the battery is charged, and fully inserted, and the door must be completely closed. Also make sure the memory card door is closed.
3) The camera does not actually need a memory card to power on. It needs a memory card to record images as you take them. But sometimes the card itself is the problem (and a bad card can prevent the camera from powering on). Remove your card, close the door to the memory card slot, and power up the camera. Does the camera power-on with no memory card inserted? If so, you've got a bad card.
4) The power switch is really a software-switch. It doesn't really cut the power to the camera. It sends a signal to the camera that tells it to power-off and being "powered off" is really a kind of extended sleep. When you use the power-swtich to turn the camera "on" what you are really doing is telling the camera to come out of that extended sleep mode. The camera does not actually boot up. The camera REALLY boots up when you insert a battery. I suggest you make the changes above (remove all 3rd party accessories, remove the lens (and attach the dust cap), remove the memory card (and close the door), then as a last step... remove the battery... wait several seconds... then re-insert the battery, close the door, and attempt to power-up the camera body.
Let us know if any of that helped resolve the issue.
If no... then the camera probably needs attention from a qualified Canon service center.
Tim Campbell
5D III, 5D IV, 60Da
