Theming login page--user--login.tpl.php
When using page--user--login.tpl.php you have to manually fetch the user login form, as your overriding the entire page template not just the form.

You can either include this directly in the template (along with any other markup):

print drupal_render(drupal_get_form('user_login'));


Or in your mxblog_preprocess_user_login() function must return the form:

function mxblog_preprocess_user_login(&amp;$variables){
  $variables['form'] = drupal_get_form('user_login');
}


then in the template you should be able to to do as you want:

print drupal_render($form['name']);
print drupal_render($form['pass']);
print drupal_render($form['form_build_id']);
print drupal_render($form['form_id']);
print drupal_render($form['actions']);