Even though you are connected to the internet, it appears that the connection to our server via Studio One is not being made. Please try disabling your Windows Firewall and/or any 3rd-party Firewall that you might have installed on your system. If this resolves your issue, check your firewall settings to see if Studio One is being allowed access. If you delete all of your firewall rules for Studio One, you will be prompted to allow access when opening the program. Make sure you turn your firewall/s back on after testing for this functionality. In the event that you might have a corrupt user profile, please try creating a new user account on your computer, log into that account, and test for this functionality again.
Here is a knowledge base article for doing an offline activation for Studio One:
http://support.presonus.com/entries/68919370--4-Studio-One-3-Software-Activation-Offline-Computer-