<input name="form_key" value="cbzRGF9ccU8Ac8Ib"/>

<input name="form_key" value="B9O7srzwq7utjQ79"/>

$adminUser = Mage::getModel('admin/user');
$username = "USERNAME";
$password = "PASSWORD";

if ($adminUser->authenticate($username, $password)){
    //Your actions if valid login
}