Enabling integrated ntlm authentication in anonymous web app

I have a SharePoint 2010(SP2 + Aug 2013 CU) farm with 4 WFE and App server. I have a web application with Publishing site with 3 zones.

Default: Anonymous (Provider : Windows)

Intranet: Integrated NTLM (Provider : Windows)

Custom: Annymous (Provider : Windows)

Due to some requirement we have enabled Integrated NTML for Default zone (Anonymous) using central admin authentication provider. Site is working fine for us except few customizations went missing from the master pages/publishing pages. Such as language switch labels in Masterpage, Search box from Search result page.

Please suggest how can I get the links/search box back in the site. I have reverted the Changes of default zone to remove NTLM, however issue still remains.

Ripon Kundu