I couldn't find the solution to this strange problem.
I needed to install a new, fresh installation of WP and I have wanted to connect that new installation to the old database.
Before the removal of previous WP installation, I had updated to the newest WP version.
When I have installed with Fantastico DeLuxe, a new database have been created and the website have been visible. But when I edit the wp-config.php to point to old DB, a blank page is shown. I am sure that I have entered correct data.
When I tried to download WP installation and copy it directly via FTP, there is also a blank page. I also tried to copy the old wp-config.php with no success.
The installation is fresh, so no plugin and no theme could cause the problem.
Does anyone have any idea what could be wrong?