I'm almost willing to bet the issue lies on that exclamation point in your WiFI signal-strength meter; this is Android's way of saying "I am connected to this WiFi point, but because it's apparently not passing any traffic" (because you hadn't logged in yet) "I'm going to ignore this network until I see that it works" (until you log in/etc.)

So you should either pull down notification bar and hit "Log into the network", and if that still doesn't work, go to Settings->Connections->WiFi->Advanced->Switch to Mobile Data->Network Exceptions and add this WiFi network to that; it'll then stay connected no matter what.

Thirdly, the best site to use to get past captive portals is "NeverSSL.com". As the name implies, it doesn't do SSL connections (and therefore the multiple handshakes necessary to validate, which won't work on a connection like yours that's not logged in). The portal will redirect you to a login/code page.