1D MKiii no control over shutter speed in Av, Tv, or P modes

Hi there,
I seem to have a problem with my 1D MKIII wherein if shooting in Av mode the shutter speed stays locked on 8000 no matter the ISO or aperture setting. I have a 100-400 EF attached. Pictures come out black because the shutter speed is too fast. I realize the shutter speed is set by the camera in Av mode, but why will it not behave and change with a change in ISO or Aperture? All functions are set to recommended defaults.
After some discussion, I reset the camera with a new button battery, set the date etc...Then I upgraded the firmware from 1.3.0 to 1.3.2, checked all functions in Cfn OK.

Manual mode does work, except the exposure meter on the side does not seem to be working, i.e. while adjusting you do not see any movement, no little square moving up or down.

Also, in Av, you can change the aperture, but as soon as you half press the shutter, it reverts to 22 and 8000. I set the upper limit to 1000 as a test, but goes right to 8000 anyway.

I love this old beast and would hate to see it die since Canon no longer supports it.

Help if you can.

Obviously the light meter has gone bonkers. It thinks you are aiming the camera directly towards the sun all the time.
Hence no reaction in manual mode either, as it still thinks it's too bright, even if you would put the lens cap on.