if else header statement twentyten

I just cannot get ‘header.php’ on front page and ‘header_inside.php’ on the rest of the pages/posts. I know I am doing something wrong but I am lost. I have a static front page called ‘Playground’. Any help (clear code) would be welcome. Thank you.

This is the code on the index.php page (all is in child theme)

[code moderated - please use the pastebin.com for any code longer than 10 lines]