Is there ANY way to remove comments function and section totally?

// Disable support for comments and trackbacks in post types
function df_disable_comments_post_types_support() {
    $post_types = get_post_types();
    foreach ($post_types as $post_type) {
        if(post_type_supports($post_type, 'comments')) {
            remove_post_type_support($post_type, 'comments');
            remove_post_type_support($post_type, 'trackbacks');
        }
    }
}
add_action('admin_init', 'df_disable_comments_post_types_support');

// Close comments on the front-end
function df_disable_comments_status() {
    return false;
}
add_filter('comments_open', 'df_disable_comments_status', 20, 2);
add_filter('pings_open', 'df_disable_comments_status', 20, 2);

// Hide existing comments
function df_disable_comments_hide_existing_comments($comments) {
    $comments = array();
    return $comments;
}
add_filter('comments_array', 'df_disable_comments_hide_existing_comments', 10, 2);

// Remove comments page in menu
function df_disable_comments_admin_menu() {
    remove_menu_page('edit-comments.php');
}
add_action('admin_menu', 'df_disable_comments_admin_menu');

// Redirect any user trying to access comments page
function df_disable_comments_admin_menu_redirect() {
    global $pagenow;
    if ($pagenow === 'edit-comments.php') {
        wp_redirect(admin_url()); exit;
    }
}
add_action('admin_init', 'df_disable_comments_admin_menu_redirect');

// Remove comments metabox from dashboard
function df_disable_comments_dashboard() {
    remove_meta_box('dashboard_recent_comments', 'dashboard', 'normal');
}
add_action('admin_init', 'df_disable_comments_dashboard');

// Remove comments links from admin bar
function df_disable_comments_admin_bar() {
    if (is_admin_bar_showing()) {
        remove_action('admin_bar_menu', 'wp_admin_bar_comments_menu', 60);
    }
}
add_action('init', 'df_disable_comments_admin_bar');

Source

There's an out-of-the-box solution that does just that. It's a plugin from Frank Bültge

Docs: http://wpengineer.com/2230/removing-comments-absolutely-wordpress/

Plug-in download: https://github.com/bueltge/Remove-Comments-Absolutely

Just install, and thats it. no config.

It works fine with WP 3.5

Here is a list of all of the above answers and a removal of the admin bar link. Just add it to your themes function file or make it a plugin. I will mark this as a community wiki as everyone's answer is right just no one added it all together.

<?php
// Removes from admin menu
add_action( 'admin_menu', 'my_remove_admin_menus' );
function my_remove_admin_menus() {
    remove_menu_page( 'edit-comments.php' );
}
// Removes from post and pages
add_action('init', 'remove_comment_support', 100);

function remove_comment_support() {
    remove_post_type_support( 'post', 'comments' );
    remove_post_type_support( 'page', 'comments' );
}
// Removes from admin bar
function mytheme_admin_bar_render() {
    global $wp_admin_bar;
    $wp_admin_bar->remove_menu('comments');
}
add_action( 'wp_before_admin_bar_render', 'mytheme_admin_bar_render' );
?>

This should remove support for comments on your site:

add_action('admin_menu', 'remove_comment_support');

function remove_comment_support() {
    remove_post_type_support( 'post', 'comments' );
    remove_post_type_support( 'page', 'comments' );
}

I don't know if it will hide every mention of comments in the admin section, though. The "Right Now" box on the dashboard is mostly hard-coded, so you'd have to hide that box or do some hackery to filter out the line about "Comments". But it should remove the "comments" text everywhere else that I can think of.

This will not remove it from your markup per se, but you can easily hide the WP 3.1 admin bar link (both visually and from screen-readers) by adding the following line to your theme's CSS:

li#wp-admin-bar-comments { display: none; visibility: hidden; }

To remove the Comments menu:

add_action( 'admin_init', 'my_remove_admin_menus' );
function my_remove_admin_menus() {
    remove_menu_page( 'edit-comments.php' );
}