My internet is working fine, I can't sign in to the PSN, is anyone else able to sign in? Right now it's June 8, 2013 at about 10 AM CST.
PSN is not down, no.
Also I'm signed in & playing online right now, the issue must be a 'local' one to you.
I had to put my PS4 ub StandBy and then restart in order to get on.