Internet Explorer is a dependency of League of Legends. Many facets of League of Legends, including the store and login screen, are affected by your Internet Explorer settings. This is true even if you have a different default browser. For this reason, many common errors with the PVP.Net portion of League of Legends can be resolved by restoring your Internet Explorer settings to default.
After clicking on the store button your PVP.Net window looks like this
Enable TLS 1.0 and SSL 3.0 in Internet Explorer (#1 Solution)