Unable to start Windows apps (application of unknown origin)

Opening any app on Windows 8.1 Enterprise will give me the following error:

This app can't open

There's a problem with [App]. Contact your system administrator about repairing or reinstalling it.

In the Microsoft-Windows-TWinUI/Operational event log there's a corresponding log message:

Activation of the app [App] for the Windows.Launch contract was blocked with error 0x80073CFC because its package is in state: Error from application of unknown origin.

So what's an application of unknown origin and how can I overcome this problem? Am I missing some certificate here? All of those apps were installed using the Windows Store, so nothing special here ...

Update: Message in the system event log

Unable to start a DCOM Server: Microsoft.WindowsLive.Mail.wwa as Unavailable/Unavailable. The error: "15612" Happened while starting this command: "C:\Windows\system32\wwahost.exe" -ServerName:Microsoft.WindowsLive.Mail.wwa