When trying to update apps from the Windows Store and they fail with the error "Something unexpected happened Code: 0x800706D9" it is usually due to the necessary Windows services not running.
To fix this ensure the following services are running:
Background Intelligent Transfer Service
Cryptographic Services
Storage Service
Windows Installer
Windows Update
(If you are not familiar with Windows Services you can open them by clicking on the Start Menu and type "services.msc" without the quotes.)