Dashboard Whitescreen of Death?

I can login into the Dashboard and see the menu of the left, it shows that there are 7 plugin updates and a WordPress update required but on the right I have a blank screen, I can see the update to WordPress button along the top but when you click on it nothing happens. I have read several posts and update the config file to true to show debug, this is the result:

Notice: wp_enqueue_style was called incorrectly. Scripts and styles
should not be registered or enqueued until the wp_enqueue_scripts,
admin_enqueue_scripts, or init hooks. Please see Debugging in
WordPress for more information. (This message was added in version
3.3.) in /home/breinton/public_html/wp-includes/functions.php on line 3587

Notice: wp_enqueue_script was called incorrectly. Scripts and styles
should not be registered or enqueued until the wp_enqueue_scripts,
admin_enqueue_scripts, or init hooks. Please see Debugging in
WordPress for more information. (This message was added in version
3.3.) in /home/breinton/public_html/wp-includes/functions.php on line 3587

Notice: register_sidebar_widget is deprecated since version 2.8! Use
wp_register_sidebar_widget() instead. in
/home/breinton/public_html/wp-includes/functions.php on line 3467

Notice: register_widget_control is deprecated since version 2.8! Use
wp_register_widget_control() instead. in
/home/breinton/public_html/wp-includes/functions.php on line 3467

Any help or advice on how to fix this and update the WordPress without loosing anything would be really appreciated.

You have active a plugin or theme, that include scripts or styles via function wp_enqueue_style and wp_enqueue_script. Since version 3.3 is it not possible to enqueue script and styles without a hook. Find the source and fix this, is easy to do that. The codex have for this topic a fine documentation.

/**
 * Proper way to enqueue scripts and styles
 */
function theme_name_scripts() {
    wp_enqueue_style( 'style-name', get_stylesheet_uri() );
    wp_enqueue_script( 'script-name', get_template_directory_uri() . '/js/example.js', array(), '1.0.0', true );
}

add_action( 'wp_enqueue_scripts', 'theme_name_scripts' );

The same problem is on the your widget topic.
To find the right plugin or theme, deactivate all plugins and switch to default theme. Switch on step by step and check.