Using phpMyAdmin I created a mySQL database and setup a User with Password. Then filled the details into wp-config.php and tried to intall WordPress. Got "Error establishing a database connection".
The trouble was that when I specified the Password in phpMyAdmin I then also clicked the "Generate Password" button. (I thought that's what I was supposed to do :-)
I did not realise that this button generates a random password, and ALSO FILLS THIS RANDOM PASSWORD into the database LogIn information overwriting the password I had entered.
That's why the database password did not match what I typed into wp-config.
Solution: Do not click buttons unless you (ie. me) understand what they do.
All works OK now.