Kaz Hirai has just announced that the PSN restoration process has begun. Right now, most users will be able to update the firmware of their PS3 and change their passwords. As for a nationwide restoring of the service, that will happen from on a state by state basis. Sony currently has a map on its blog that it will use to indicate which state has service restored. The first service to be restored for PSN will be online multiplayer. He hasn’t stated when the Playstation Store will be up and running again.
Kaz Hirai Restoration Announcement
Update 1: So far I can confirm that I was able to update to the latest firmware. I wasn’t able to change my password. It did give me a message , however, stating that my password is now invalid, so Sony is serious when they say to change the password. It was followed by a message stating that the Network is undergoing maintenance. So in due time, I’ll be able to change the password.
Update 2: After seeing that Sony has updated their restoration map (see link above), and that New York’s PSN service is on, I checked again to change my password. The first attempt game me the same message as before. But the second attempt brought me to the password change screen. And so I can confirm that PSN is up and running for the Northeast US. It’s still a bit rough though. I have yet to play a game though. I checked the PSN store, but it’s still down. I’d imagine that’s the last thing that will be turned on most of the transaction activity happens there.
The Wired Fish Network 
when will psn store be up and running again
Some are pointing to the end of the month. Since most of the sensitive info was utilized during Playstation Store transactions, I think it’ll be the lat thing they restore. For right now, there’s no official statement from Sony.