Fix Store App in Windows 8.1
http://blogs.msdn.com/b/notime/archive/2013/10/21/10458031.aspx
•Sometimes, after upgrading to Windows 8.1, the Store App may not start.
•It might still show the number of available updates on the Live Tile.
•Starting the app may show a progress ring but it may not finish loading.
•To fix this, run the following in a Command Window (CMD) to re-register the Store App:
powershell -ExecutionPolicy Unrestricted Add-AppxPackage -DisableDevelopmentMode -Register $Env:SystemRoot\WinStore\AppxManifest.xml
Do you dabble with Registry Cleaners or "Boosters"? They often cause weird problems.
Win8: App: Modern: Apps fail to start if default registry or file permissions modified
http://support.microsoft.com/kb/2798317
What if you test with another Windows user rather than the current user?
How to perform a clean boot to troubleshoot a problem in Windows Vista, Windows 7, or Windows 8
http://support.microsoft.com/default.aspx/kb/929135