Can't connect to the PlayStation Network? That's because much of the PlayStation Network is down, and will be for half the day.
Sony say the service's servers went offline at 0030 Pacific Time, and won't be back until 1230 PT, a downtime of approximately (these things are never to the minute) twelve hours.
During that time, you definitely won't be able to access the PlayStation Store or Account Management, and users "may encounter difficulty" trying to even sign into the PlayStation Network.
The downtime is for regularly scheduled maintenance, so go make yourselves useful and come back after lunch. Or dinner, depending on where you are in the world!