I have the same error on my blog (www.movienarc.com). My site has been working fine for months, then all of a sudden I got the same error you did.
Someone told me I could add some code to get a more informative error, so I did (to wp-includes/wp-db.php add echo mysql_error(); before $this->bail). Now I see the error is related to a user/password. So, going into mysql I notice the user, for whatever reason, was gone. I added the user back…but I still get the error.
I’m in the same boat as you now. Getting that error and don’t know how to fix it.