If you are connected to internet and can access web and just cannot sign in, than this may be because your company network is blocking this. Are you are behind a proxy? If yes than you will have to add proxy server credentials. In studio pro, go to ‘Edit’ from the menu and click on ‘Preferences’ > select ‘Advanced tab’ and enter proxy server details or click on ‘Proxy Settings’ link in the sign in page.
If this is not the case than I suggest to create a support ticket on support.mendix.com
Hope this helps!
The screen says you are offline… are you certain you have a connection?