EOS 5D mark 3 exposure metering problem

Question

Today, I got a problem with my 5D mark 3. I was using my 5D mark 3 and speedlite on Camera. After finished shooting, I took off the flash from the camera and shot it in Program mode (P) without flash, and auto ISO setting. I found out that my camera's exposure meter is getting wrong. The result image is too much underexposed even the metre show the exposure value 0. I changed the setting to Aperture Priority mode (Av), I still have the same problem. Then I tried the Shutter Priority mode (Tv), I still have the same problem, so I tried to shoot with Manual mode and I found out that I need to shot in five stop over to see the image. In other settings, Shutter speed is getting to high (or) the aperture is too narrow for the low light condition even when the ISO is 100.
Then I tried to shoot it while LCD is on. The exposure meter reading is correct and get the right exposure. No problem at all. But when I shoot while LCD is off, I got the problem again. Too much under exposed. I tried to shoot with flash. The result is OK. 
I think my camera is still thinking that it's attached with the flash, but I don't know how to solve the problem. I tried to reset all the setting but I still got the problem. I couldn't find any post for that problem on internet (may be I don't know how to find). 
Can anyone help me how to solve that problem ? 
Thanks & Regards
Zeal

Answer 1

Thanks for posting those images with EXIF data intact.
I recommend you contact Canon service to arrange for repair.  Your "meter" believes you are receiving an extreme or possibly infinite amount of light and isn't just metering high (and underexposing by a stop or two.)
Here's why:
Your first shot is a "manual" exposure.  
You used:
Manual
1/12 sec
f/4
ISO 10000
You would have to pick all of these settings.
Your second shot used Aperture priority.  This means you get to pick the aperture, the camera will pick the shutter speed.
Aperture priority
1/8192 sec <- camera picked this value
f/4 <- you picked this value.
ISO 10000
As you can see, the camera pixed the fastest shutter speed possible.  I suspect it would have chosen an even faster speed if only it were possible.... but 1/8192 is the limit for that camera.
Your third shot used shutter priority.
Shutter priority
1/21 sec <- you picked (you probably picked 1/20th but it got rounded by the EXIF data)
f/22 <- camera picked this... but note the high f-stop value.    That's the smallest available aperture on the lens.
ISO 10000
As you can see here, the camera tried to constrain the light as much as possible by setting the smallest aperture opening (highest f-stop value) the lens can provide.
And that brings us to your final example... Program AE
Program
1/8192 sec <- camera picked this value
f/22 <- camera picked this value too
ISO 10000
As you can see... everytime you give the camera control over the setting... it does everything it can do to cut the light.  
This is not merely an example of exposure compensation being a stop or two below standard... your camera thinks it needs to do everything it can to reduce the light.  It's as though the meter believes it is getting an infinite amount of light.
This is not a camera setting we can "adjust" (we can control the meter within a few stops).  This is an issue which would need professional repair.
Tim Campbell
5D II, 5D III, 60Da