Since no one was able to guess my issue, I copied a section of my previous themes that worked. By placing:
<link rel=”stylesheet” href=”<?php bloginfo(‘stylesheet_url’); ?>” type=”text/css” media=”screen” />
instead of what twentyten has in header.php:
<link rel=”stylesheet” type=”text/css” media=”all” href=”<?php bloginfo( ‘stylesheet_url’ ); ?>” />
I was able to solve the issue. Don’t know what css settings ruin my design, now I know how to bypass this. Maybe it’s gonna be useful to others too.