While the PlayStation Network might still be having issues to some, several forum posters on NeoGAF are reporting the ability to log into the PlayStation Network with this fix:
Go into your Network settings, and change your MTU setting to 1473, leave everything else however you had it.
Posters from several regions including Hong Kong, Australia, and North America are saying that this settings change is working for them. Give it a try and let us know if it works for you.
If it doesn’t, at least there’s always the greatest game of all time.