There is no opening <?php tag in your second (index.php) block of code.
It should look like,
<?php get_header(); ?>
<a href="wp-content/themes/twentyeleven/result.php">Main</a>
<?php get_footer(); ?>
Ammend that and try again
Edit:
I didn't read that clearly the first time around but you need to link to your Result page like this,
<a href="<?php get_the_permalink();?>/result/">Main</a>
At the top of result.php, change it to read:
<?php
/*
Template Name: Result Template
*/
get_header();
?>
//do your results stuff here... or get regular page loop.
<?php get_footer(); ?>
In your dashboard, go to Pages, Add New and enter a Title named Result.
Then from the right hand side Page Attributes meta box, select your Result Template from the drop down menu and then Publish the page.
When you visit http://www.yoursite.com/result/ your page and its content will show correctly using the result.php page template created and assigned.