aegirr on "Error establishing a database connection"

I am trying to install WordPress on my local computer but I keep getting this classic message "Error establishing a database connection".

I have tryed the following:

1. I make sure the MySQL database and the web server is running.
2. I make sure username, name of the database and password is correct.
3. I have checked wp-config.php many times for errors/typo. I have tryed this

define('DB_HOST', '127.0.0.1:3306');

and this

define('DB_HOST', '127.0.0.1:8889');

instead of this

define('DB_HOST', 'localhost');

but I still get the error-message

Any ideas?

I have actually installed WordPress on another PC many times without any errors, so why should I get this now?