I recently had this issue like you're describing when I went to render, the shadows seemed to flicker all the way through the animation. All I had were basic shapes, too. It was a computer screen and a stand, pretty boring and easy. I had a similar setup and was having a hard time just getting the shadow right for some reason. Anyway, I finally figured that if I set 2 colors for the shadow and diffuse channels then my problems seem to go away. I'm not sure if that was the ultimate solution because I also placed a light and isolated it on just the problem area (excluded that light from everything else).
I'd try playing around with light placement and maybe 2 colors. I also turned off the camera setting (you have that checked in your scene). Then again, it's what helped me to get my render going and may not even be what's wrong with yours.