Open up an elevated Powershell prompt by typing "Powershell" in Start, right-clicking on the first option, and selecting "Run as administrator." In the prompt that appears, enter this:
PowerShell -ExecutionPolicy Unrestricted -Command "& {$manifest = (Get-AppxPackage Microsoft.WindowsStore).InstallLocation + '\AppxManifest.xml' ; Add-AppxPackage -DisableDevelopmentMode -Register $manifest}"
There will be several errors that can be safely ignored. After the command completes, reboot your PC. Try running the Store again.