WIndows Store App Won't Open )-:
Welcome to Windows 8 Community!
From your issue description I understand that you are unable to open Windows 8 Store App. We have got some troubleshooting steps in order to resolve the issue.
This issue might happen because of some updates in the app.
I would suggest you to try the following methods and check if it helps to resolve the issue.
Download and run the Modern UI App troubleshooter and check.
Method 2: Check if the Date, time and Time zone is set correct.
Follow the steps to set the date and time:
a. Press Windows key + C on your keyboard to show the Charms bar.
b. Type “Date and Time” in the charms bar search.
c. Click Change date and time button.
d. Click Apply and Ok to save the date and time.
Note: Click on the Time Zone tab to check the Time Zone.
Method 3: If you are using any Proxy connection, then try disabling the proxy connection
a. Click the Gearbox at the top right corner in internet explorer.
b. Click the Tools button, and then click Internet Options.
c. Click the Connections tab, and then click LAN settings.
e) Check “Automatically detect settings.”
f) Uncheck use a proxy server for your LAN.
Method 4: Check the Windows Firewall Settings
a) Type in Control Panel on the Start Page.
b) On the left side, click Control Panel.
c) Click on Windows Firewall.
d) On the left pane, click on "Allow an app or feature through Windows Firewall".
e) Under the Allowed apps and features, look for Store.
f) Make sure you have a click in Private and or Public.
g) Then see if you can open the Windows Store.
If you have a 3rd party Firewall, you may need to change the settings to allow the app through the Firewall.
NOTE: Antivirus software can help protect your computer against viruses and other security threats. In most cases, you should not disable your antivirus software. If you have to temporarily disable it to install other software, you should re-enable it as soon as you are done. If you are connected to the Internet or a network while your antivirus software is disabled, your computer is vulnerable to attacks.
Method 5: What to do if you have problems with an app
Apps & Windows Store
Hope it helps. For any further Windows related assistance, feel free to contact us and we will be happy to help.