Startup your PS4 and navigate to New User >> Create a User or User 1 on the PlayStation Log-in screen. Create a new user option; This should create the local user on the PS4 itself, not a PSN account. Select Next >> New to PlayStation Network? Create an Account > Sign Up Now.

Get help with PlayStation 4 connection issues. Our fix & connect tool offers support if you can’t connect to the Internet, sign in to PSN or your online experience is poor. Can't sign into PlayStation store on my laptop. : PS4 The largest PlayStation 4 community on the internet. Your hub for everything related to PS4 including games, news, reviews, discussion, questions, videos, and screenshots. 3.4m I cant log in to my account? - PlayStation Portable Q&A

I had the same problem. It turns out that the problem is that the PSP fixes user IDs to itself. You can gsign in via another ID if you delete the account from the PSP (don't worry, it will only remove it from your PSP);

How to know if my PSN account is logged into another Sony It doesn’t say if you’re signed in at the time. But it will show you a list of currently active devices and you can deactivate them. Also from this page it says. How more than one user can sign into PlayStation Network on one PlayStation syst

For PlayStation 3 on the PlayStation 3, a GameFAQs Q&A question titled "Why cant I sign into my Playstation@Network account?".

Why can't I log in to my Sony Entertainment Network Jan 25, 2008 Sign In/Sign Out | PlayStation®Vita User's Guide