installation error (database problem)

Hi everybody!
I have just installed an apache server on my computer to test wordpress before I get my own webspace. I have the apache server and mysql database running. So far I have tested the server with various php sites and yes it displays them – so the server is working (it’s by the way the latest release).
Then I have downloaded wordpress and copied everything into the “htdocs” folder of the apache installation. I hope this is right, because you have to copy all *.php files into the “htdocs” folder to load them in your browser with the “http://localhost/xyz.php” command. So I though I have to copy the wordpress folder into that directory as well.
Then I edited the wp-config (acutally I have left everything the way it was):
<?php
/** WordPress’s config file **/
/** http://wordpress.org/ **/
// ** MySQL settings ** //
define(‘DB_NAME’, ‘wordpress’); // The name of the database
define(‘DB_USER’, ‘username’); // Your MySQL username
define(‘DB_PASSWORD’, ‘password’); // …and password
define(‘DB_HOST’, ‘localhost’); // 99% chance you won’t need to change this value
.
.
.
?>
Then I tried to execute the install.php (http://localhost/wp-admin/install.php) and I got this error message:
Error establishing a database connection! This probably means that the connection information in your wp-config.php file is incorrect. Double check it and try again.
* Are you sure you have the correct user/password?
* Are you sure that you have typed the correct hostname?
* Are you sure that the database server is running?
————–
So what does this mean? Can someone help me out? Thanks for every tip!
Bye
Phil