Missing MySQL extension after changing host

Hello!
I’ve tried to change host for my webpage, and before I got the new host a took a complete bakcup of both my page and the database. When I got my ny web-hotel a copied all of the info, imported the database and updated the wp-config.php with my new DB-info.

My webpages is showing perfectly, but I’m having great issues with loggin in. In the beginning I just got a white page when trying to access the wp-login, but now the wp-login shows up. But, when I try to login I just get this message:
“Your PHP installation appears to be missing the MySQL extension which is required by WordPress.”

I’ve double- and triplechecked – that there is no white-space in the beginning or in the end of my .php-files.

I’m using the twenty-eleven theme (child)

When enabling the debug, i get the following errors on the main page:

Notice: rss.php is deprecated since version 3.0! Use wp-includes/class-simplepie.php instead. in /home/3/b/***/www/***/wp-includes/functions.php on line 2745

Notice: add_custom_background is deprecated since version 3.4! Use add_theme_support( ‘custom-background’, $args ) instead. in /home/3/b/***/www/***/wp-includes/functions.php on line 2705

Notice: add_custom_image_header is deprecated since version 3.4! Use add_theme_support( ‘custom-header’, $args ) instead. in /home/3/b/***/www/***/wp-includes/functions.php on line 2705

The line 2745 equals:
* @param array $args An array of key => value arguments to match against each object
The line 2705 equals:
$function, $version, $replacement ) );

On my wp-login.php I get the following errors:
Notice: rss.php is deprecated since version 3.0! Use wp-includes/class-simplepie.php instead. in /home/3/b/**/www/**/wp-includes/functions.php on line 2745

Notice: add_custom_background is deprecated since version 3.4! Use add_theme_support( ‘custom-background’, $args ) instead. in /home/3/b/**/www/***/wp-includes/functions.php on line 2705

Notice: add_custom_image_header is deprecated since version 3.4! Use add_theme_support( ‘custom-header’, $args ) instead. in /home/3/b/***/www/***/wp-includes/functions.php on line 2705

Warning: Cannot modify header information – headers already sent by (output started at /home/3/b/***/www/***/wp-includes/functions.php:2745) in /home/3/b/bjoerkli/www/nalle/wp-login.php on line 365

Warning: Cannot modify header information – headers already sent by (output started at /home/3/b/***/www/***/wp-includes/functions.php:2745) in /home/3/b/***/www/***/wp-login.php on line 377

Line 377 in wp-login.php equals:
setcookie(TEST_COOKIE, 'WP Cookie check', 0, COOKIEPATH, COOKIE_DOMAIN);

And finally, when I’ve entered my username and password I get this message (when debug is activated):

Notice: add_custom_background is deprecated since version 3.4! Use add_theme_support( ‘custom-background’, $args ) instead. in /home/3/b/***/www/***/wp-includes/functions.php on line 2705

Notice: add_custom_image_header is deprecated since version 3.4! Use add_theme_support( ‘custom-header’, $args ) instead. in /home/3/b/***/www/***/wp-includes/functions.php on line 2705

Warning: Cannot modify header information – headers already sent by (output started at /home/3/b/***/www/***/wp-includes/functions.php:2705) in /home/3/b/bjoerkli/www/nalle/wp-login.php on line 365

Warning: Cannot modify header information – headers already sent by (output started at /home/3/b/***/www/***/wp-includes/functions.php:2705) in /home/3/b/***/www/***/wp-login.php on line 377

Warning: Cannot modify header information – headers already sent by (output started at /home/3/b/***/www/***/wp-includes/functions.php:2705) in /home/3/b/***/www/***/wp-includes/pluggable.php on line 680

Warning: Cannot modify header information – headers already sent by (output started at /home/3/b/***/www/***/wp-includes/functions.php:2705) in /home/3/b/***/www/***/wp-includes/pluggable.php on line 681

Warning: Cannot modify header information – headers already sent by (output started at /home/3/b/***/www/***/wp-includes/functions.php:2705) in /home/3/b/***/www/***/wp-includes/pluggable.php on line 682

Warning: Cannot modify header information – headers already sent by (output started at /home/3/b/***/www/***/wp-includes/functions.php:2705) in /home/3/b/***/www/***/wp-includes/pluggable.php on line 881

I have removed all my plugins – but not akismet.

I’ve been as specific as I can be. Does anyone have any suggestions?