People reported me this particular problem, and recently I experienced it myself: during the Drupal 6 installation process in the 'Database configuration' step, you might get stuck. Upon entering the right database credentials, the page reloads and shows the Database configuration form again, without any error.
After some searching around, I found what was causing this behaviour:
During the installation I renamed the file /sites/default/default.settings.php to /sites/default/settings.php.
However, Drupal expects you to make a copy if this file, not rename it!
So just make a copy of the default.settings.php file, and name it settings.php.
When these 2 files are available, your installation should run without any problems.