After following the installation instructions by the letter and staring at my wp-config file until I was crosseyed, the thing still couldn't "establish a connection with the database" that I knew for a fact was there.
What was the trouble? White space. On a hunch, I deleted all the comments in the wp-config.php file (the // and everything after until end of each line)
Lo and behold. It worked. I'm up and running.