Cannot play neither IE10 HTML5 video nor Modern UI apps video
In Agreement with Velcro answer
I uninstalled the driver of my ATI Mobility Radeon HD 3670 and removed the graphic card itself (including drivers by selecting the checkbox) in the Device Manager. Then, I let Windows to install its own drivers for this card.
The graphic card label now contains WDDM v1.1. I'm pretty sure there is a causal relationship between that, Media Foundation and MPEG-4 video playing...
I disabled GPU rendering in IE (Internet Options > Advanced > Accelerated graphics > Use software rendering instead of GPU rendering) and it played html5 video succesfully.