Go to Control Panel, find Wireless Network Connection - there should be options to Disable/Enable the Adapter, and under it - Connect/Disconnect ... it should display the SSID that you are connected to.

Play around with those and while you are at it - with adapter enabled, launch Command Prompt & run IPCONFIG release, then renew - or better yet, power cycle the laptop/notebook. Reconnect with your alternate browser (Chrome vs. Firefox, etc.) and clear/flush cookies & cache, if any from previous session - and reconnect to see if you can get the "Welcome" screen