If you’ve found that particular transients simply will not display in your theme yet they aren’t throwing an error?  Check your database for duplicate entries.  It is possible when moving a site between servers for a transients to become duplicated within the wp_sitemeta table and this causes the get_site_transient() function to silently fail.  Simply go in and remove the duplicate transient ‘meta_key’s that are LOWER than the highest duplicate.  After doing this you should now see your transients correctly.