It seems major connection issues have occurred since the game went live. One of the main problems on launch day was an endless loading screen. The studio deployed an update which addressed the issue.
The problem was “rooted in the login and authentication servers,” not the actual game servers. The Farm 51 said it is continuing to work on mending connection issues and other problems as they arise, and will release small updates once fixed.
While some Early Access players have been able to get into the game today, others are still experiencing issues. This has kicked off World War 3 (bad pun intended) on the Steam forums, as many are having kittens because the World War 3 early access launch didn’t go smoothly. Cooler heads on the matter have called on others to be patient as The Farm 51 is working almost beyond capacity to fix the problem.
In other words, STEAM is not validating your purchase of the game allowing you to join the servers. Check your global stats in store. It will say you have not purchased the game.