There are several reports from users running Windows 8.1 about the Store not working.
You can try to Run Apps Troubleshooter
Download and run the Modern UI App troubleshooter and check.
http://download.microsoft.com/download/F/2/4/F2...
Please use the following links as a reference :
http://windows.microsoft.com/en-us/windows-8/wh...
If that does not work, try performing a repair upgrade:
Download the Windows 8.1 ISO:
Download Windows 8.1 Disc Image (ISO File) - Microsoft
https://www.microsoft.com/en-us/software-downlo...
Perform a repair upgrade: