I experienced the same issue. I’ve read through the posts and will attempt to follow-up.
As a bit more…I first experienced this issue on my blog on 8/18 after my provider automatically upgraded the WP release.
After attempting to restore prior files based on prior server backups, I deleted the entire WP blog, and then established a brand new one based on the latest release, then painfully restored my content.
Everything worked fine and I made a few additions. On 8/19, everything worked fine. On 8/20, I experienced the WP “Error establishing a databased connection.” That was the same issue first encountered on 8/18. This time I checked and SBC/AT&T showed my database as active. I have asked my provider for feedback on their side, but have not received a reply.
Again, I’ll work through the prior posts, but I would like to find the root cause given the prior rebuild.