Moving site to new domain on the same server
Check your .htaccess

Open your htaccess and modify line 94 to match your needs.  

  # Modify the RewriteBase if you are using Drupal in a subdirectory or in a
  # VirtualDocumentRoot and the rewrite rules are not working properly.
  # For example if your site is at http://example.com/drupal uncomment and
  # modify the following line:
  RewriteBase /YOUR-FOLDER-NAME
  #
  # If your site is running in a VirtualDocumentRoot at http://example.com/,
  # uncomment the following line:
  # RewriteBase /


If this not work the problem is with your cache tables or custom code in template.php or in .module files

To clear cache tables you can try 

drush cc all


OR Try this in phpMyAdmin or mysql console.

TRUNCATE `cache`;
TRUNCATE `cache_block`;
TRUNCATE `cache_bootstrap`;
TRUNCATE `cache_field`;
TRUNCATE `cache_filter`;
TRUNCATE `cache_form`;
TRUNCATE `cache_image`;
TRUNCATE `cache_libraries`;
TRUNCATE `cache_menu`;
TRUNCATE `cache_page`;
TRUNCATE `cache_path`;
TRUNCATE `cache_rules`;
TRUNCATE `cache_token`;
TRUNCATE `cache_views`;
TRUNCATE `cache_views_data`;


Make sure you include all tables starting with CACHE_

More info here Can any of the cache_* be emptied safely?