I just bought this camera, and the past couple times that I have used it, the shutterspeed and iso cannot be changed in the manuel setting, unless you go into the menu through the "Q" button.
My camera settings aren't locked, (with the lock button on the camera) and the aperature can still be adjusted with the wheel. Sometimes, when I turn the camera off, take out the batteries and the memory card, it will all funciton for a couple minutes. Other times, they still don't work.
I'm using Canon batteries.
I don't know what else to do, if I need to send it in and have it replaced. A photographer told me there is a hidden reset in the camera, or that I could try and download canon's firmware.
I don't have a 6D body, but I can think of a few things to check.
Is this camera truly "new" (you are first owner) or was it previously used by someone else?
It is actually possible to re-map the functionality of many of the buttons and dials on the camera body and I'm wondering if these have been changed.
See this article: http://support-au.canon.com.au/contents/AU/EN/8201706000.html
If you follow through the steps, you'll note that there is a screen (I think it's in step 5) in which you can reset all controls to factory defaults (by pressing the trash can icon on that screen.)
You may want to reset your camera and see if that doesn't help improve things.
You may also want to reset all other camera settings... you can do that by following these instructions: