Want to exclude slider from page.php in header

Did you consult the is_page_template() Codex entry?

If you want to query for the page.php page template, then you need to pass that filename to is_page_template(); i.e.:

<?php
if ( ! is_page_template( 'page.php' ) ) {
    // The current page template is NOT page.php;
    // do something
}
?>

Sidenote: if you want to query for being a static page AND not a specific page template:

<?php
if ( is_page() && ! is_page_template( 'page.php' ) ) {
    // Current page is a static page AND
    // The current page template is NOT page.php;
    // do something
}
?>