Alright it finally let me post lol. So I just had the same problem, but as I was scrolling through the forums to see if I could find an answer it found itself. Basically the game is trying to connect to the network before letting you play. After about 5 minutes of waiting after I hit the ply game button a pop up showed up and said "could not connect to network. Continue playing offline?" Then It worked fine. I hope this is of help.
Sony has been the target of a lot of attacks on a very large scale over the past few weeks from DDoS and hacker groups protesting the company. If you received your new PS4 this morning or even last night and have been unable to connect to PlayStation Network or other aspects of the PS4, please be patient as this is something that we are all dealing with.
It's unfortunate that we as gamers have become the collateral damage of protesters and hacktivists, but these things happen and there's nothing we can do about it. I know many of you are excited to plug in and play your new games for the first time, but you're not alone. Xbox is going though the same thing, although because Microsoft has a much larger network infrastructure, the problems aren't nearly as widespread.
Being someone who's worked with networking and server maintenance before, an attack of this scale, from potentially hundreds of thousands of people in different countries isn't exactly something that Sony, or any company, can just quickly fix and keep from happening.
TL;DR: Sony is under attack by hackers, so their network including DRN check for games might be offline.