Reports are still scattered, but after testing our own PS3, it appears the that left most non-Slim PS3 consoles essentially unplayable seems to be fixed. We're guessing this issue was corrected on the server side of things, as there was no update or download required; our console just worked.
Even better, all trophy and game save data remains intact, so worries about corrupted information can be put to rest.
We still don't have an official word from Sony, but it looks like the worst is behind us. That said, we'd still recommend waiting for the all-clear sign from Sony until you boot up your console. We'll update this post when that happens.
UPDATE (10:15 p.m. ET): From Sony: "We are aware that the internal clock functionality in the PS3 units other than the slim model, recognized the year 2010 as a leap year." That's right, all non-slim PS3s thought this year had 29 days in February. Because of that incorrect programming, they couldn't communicate properly with Sony's PSN servers.
Perhaps even more upsetting is that when Sony said "we hope to resolve this problem within the next 24 hours," they really were just waiting for the next day to come so that the issue would correct itself. Needless to say, we're not looking forward to PS3 gaming in February 2012, when the real leap year will be observed.