The firewall port the PlayStation store uses isn't being opened by your router's UPnP function, solution is to either open the ports PSN uses or setup a DMZ.
When you cannot connect to PlayStation™Network
Use PlayStation™Network to connect your PS4™ system to a PlayStation™Network server or to another PS4™ system. When you're using PlayStation™Network at an office or other location with a shared network, a firewall or other security measures might prevent your PS4™ system from connecting to PlayStation™Network. If this occurs, refer to the port numbers listed below, which are used when you connect your PS4™ system to a PlayStation™Network server.
- TCP: 80, 443, 3478, 3479, 3480
- UDP: 3478, 3479
For online activities such as competing with other players while your system is connected directly to other PS4™ systems, a different port number is used each time you connect.
http://manuals.playstation.net/document/gb/ps4/settings/nw_test.html
Depending on the make and model of router and when it was first available like the original Virgin Media Superhub the above fixes may not work.