Add the following code to a file in your wordpress root and go to that page.
<?php
define('WP_USE_THEMES', false);
require('wp-blog-header.php');
$role = get_role('administrator');
echo '<pre>';
print_r($role);
echo '</pre>';
Now, look for [update_core] in the text displayed. It's value should be 1.
If not, add the following line after the $role = get_role('administrator') line to add the update_core capability to the administrator.
$role->add_cap( 'update_core' );
Reload the page to see if the value of [update_core] is 1. If it is 1, you can try to do the update. Don't forget to delete the file you've added afterwards.
Method 2:
Get on PHPMyadmin and go to the wp_users table. Look for your user ID. Now go to wp_usermeta and change the wp_capabilities of your user ID to a:1:{s:13:"administrator";b:1;}. Do a backup before touching the database, just in case.