If the PlayStation Network Status indicator says the network is up and functioning and you can't login, you may need to run through some troubleshooting to get back online. Check out the issue and steps below.
Login Issues from Your PS4™
1. Log out off your PS4™ console (the account that's having the connection issue).
2. Power down (turn off) your PS4™ console.
3. Go to PlayStation.com via a web browser from your PC or Mac. If you are currently signed in, you must sign out and then sign back in. Confirm you are are signed in. Then log out.
3.1 From Mobile devices using a web browser
For Apple phone: hold down the refresh button on the URL and click on “Request Desktop Site."
For Android: click on the 3 dots on the top right corner click on “Desktop Site."
4. Login and out a second time. Confirm you are are signed in. Then log out.
5. Go to your PS4™ console, turn it on, and login.
You will know the steps worked if you can login to your PS4, with your account.