One thing I've seen help a great deal with WP and database speed is to clean your database of post and page revisions. WP keeps a full copy of each edit revision, and with 2000 posts, your database could be huge. Run this as an SQL query in phpmyadmin to clear revisions. I've seen databases drop 75% in size and run much faster after clearing revisions. Change the table prefix if you changed it when you installed WP, and run a backup beforehand.
DELETE a,b,c
FROM wp_posts a
LEFT JOIN wp_term_relationships b ON (a.ID = b.object_id)
LEFT JOIN wp_postmeta c ON (a.ID = c.post_id)
WHERE a.post_type = 'revision'
Then optimize tables after you run that query to finish clearing the revisions, either from the dropdown menu in phpmyadmin to optimize the whole database, or by another query just for the posts table:
OPTIMIZE TABLE wp_posts;
Then you can prevent post/page revisions from accumulating again by adding this line to wp-config.php to stop revisions:
define ('WP_POST_REVISIONS', FALSE);
Or this line to select the number of revisions to keep:
define('WP_POST_REVISIONS', 3);
If you have access to your MySQL config file, look into tuning MySQL for better performance with a utility like GitHub - major/MySQLTuner-perl.