Without seeing the code, I would guess that your main stylesheet is being loaded by get_stylesheet_directory_uri() or something of that nature. Now that you’ve copied header.php into your child theme get_stylesheet_directory_uri() is looking in YOUR theme for that stylesheet. It isn’t there and thus you have no CSS. Change the stylesheet directory to get_template_directory_uri() and it should come back.
Again, this is totally just a guess since you didn’t post anything to go by. Please get in the habit of posting code as it will help us help you.