Such a common problem but there are a few different solutions to fix the issue. I wouldn't put up with the store not working for even a single day and yes I've had this problem in the past, if all else fails then a refresh or reset would most likely fix the issue.
I'm wondering David, did this system pass both the sfc and the DISM scans?
This link shows solutions that have worked in the past. >
Fix Windows 8 App Store won?t connect to Internet issue | Microsoft Surface tablet
How to fix app store won’t connect issues
* Open Internet Explorer, click on the gear icon at the top right of the screen, and select “Internet Options” from the menu. Go to Connections tab, click the LAN Settings > uncheck “Use a proxy server for your LAN box (There settings will not apply to dial-up or VPN connections).
* Press Windows + C Keys, type “Date and Time” and open the system clock. Make sure you have setup to the correct time. Then log off your account and then log in again.
* If you have installed Kaspersky or Norton 360, you need to trust app.html with firewall setting or uninstall the software completely using the special tool.