Drupal 7 multisite setup white screen
It is impossible to tell you exactly what is wrong with the information that is given.  I run several multi-sites using separate databases, and they work as advertised when I set them up following the standard instructions.

The White Screen of Death is usually caused by some error in the PHP.  To see the error message, you need to turn on PHP error reporting.  To do this, add the following to the settings.php, just below the initial &lt;?php:

error_reporting(E_ALL);
ini_set('display_errors', TRUE);
ini_set('display_startup_errors', TRUE);


This will usually show an error message that tells you where you've left out a semicolon or some other trivial PHP-error.

See also: https://drupal.org/node/1056468 and https://drupal.org/node/158043