once more Database Error

I can’t get my WordPress installation running due to a error establishing a database connection.

I want to run WordPress locally on my …
Apache 1.3 Webserver
MySQL server version: 4.1.22-max
PHP Version 4.3.11

I’ve created a database for the blog and here is how I’ve configured Mysql

My-Computer:~ mycomp$ mysql -h localhost -u root -p
Enter password:
Welcome to the MySQL monitor. Commands end with ; or g.
Your MySQL connection id is 315 to server version: 4.1.22-max
Type 'help;' or 'h' for help. Type 'c' to clear the buffer.
mysql> CREATE DATABASE blog;
Query OK, 1 row affected (0.00 sec)
mysql> SHOW DATABASES;
+----------+
| Database |
+----------+
| blog |
| mysql |
| test |
+----------+
3 rows in set (0.00 sec)
mysql> GRANT ALL PRIVILEGES ON blog.* TO "root"@"localhost"
-> IDENTIFIED BY "blogspass";
Query OK, 0 rows affected (0.00 sec)
mysql> FLUSH PRIVILEGES;
Query OK, 0 rows affected (0.00 sec)
mysql> EXIT
Bye

Now here is what I’ve put in the wp_config.php:

<?php
// ** MySQL settings ** //
define('DB_NAME', 'blog'); // The name of the database
define('DB_USER', 'root'); // Your MySQL username
define('DB_PASSWORD', 'blogspass'); // ...and password
define('DB_HOST', 'localhost'); // 99% chance you won't need to change this value

The MySQL database server IS RUNNING, but still if I want to access the /wp-admin/install.php this is want I get:

establishing a database connection
This either means that the username and password information in your wp-config.php file is incorrect or we can't contact the database server at localhost. This could mean your host's database server is down.
Are you sure you have the correct username and password?
Are you sure that you have typed the correct hostname?
Are you sure that the database server is running?

Can anyone give me a hint please?