The Playstation Store is available again on the PSN and has been updated. See http://blog.us.playstation.com/2011/06/01/playstation-store-is-available-and-updated-now/comment-page-2/#comments for more details.
However, there are two things to note.
1) The Welcome Back offer isn’t live yet, and they’re likely waiting for #2 for it.
2) It isn’t stable. I get ‘An error has occurred.’ about half the time I try and do anything on the PSN so far. But that’s to be expected, right after it comes back up.
Update: It seems to be a lot more stable now. Most likely was just a traffic issue. Welcome back offer still not available. My prediction: They’ll add something to it as a surprise and announce it at E3 as a part of their apology.
Turns out I was wrong! As my second update – The Welcome Back offer is live! See http://www.tgr-net.com/2011/05/psn-back-north-american-compensation-package/ for more details on that.