From the screenshots you've provided, it looks like the issue may be that you still have TLS 1.0 enabled.
As the link you provided about TLS 1.0 being phased out states, all sandboxes were made to require TLS 1.1 or TLS 1.2 in June of this year (2016).
My knowledge of how browsers and servers negotiate which security scheme to use is basically non-existent (sounds like something we might find on stackoverflow or another stackexchange site).
I'd think that your browser and Salesforce would negotiate to find the lowest acceptable common scheme (TLS 1.1 in this case), but perhaps the very act of suggesting TLS 1.0 as a possibility is causing Salesforce to flat out reject the connection.
Try disabling TLS 1.0, and trying to log into your sandbox again.