I am having the same problem, viewing MP4 video. Sound, but no picture. All was ok viewing on December 26, 2013 but last night I tried to make a movie, didn't work, WMM said the file was corrupted. I couldn't view it in WL Photo Gallery but I could on RealPlayer. I did as you said above and got this below.
AMD Radeon 7400 HD Series
Version 13.251.0.0
Date: 13/12/2013
Does this "seem out of date" to you?
Should I uninstall, then reinstall Windows Live Essentials? I tried the Repair, which worked in the past when there was a problem accessing Skydrive, but it did nothing for me on this.