Wordpress - Enable page templates. How?

Chances are that the theme you've switched to has no page templates defined - they exist on a per theme basis.

Here's the Codex reference: http://codex.wordpress.org/Pages#Page_Templates

Define your template name in the custom template file.

  <?php
/*
Template Name: demo
*/
?>

After this the select template option will be available on the edit screen. You can choose the desired name you want.