Problem: You discoved that on your SharePoint 2013 Foundation server, the Search WebPart disappeared. That means the user has no search option any longer when browsing the site collection. The central search also produce an error message if a user try to use it.
Solution: This is a known issue which appears when SharePoint 2013 SP1 is installed. The issue is solved in the March 2014 PU (PU=Public Update, its not an CU!) as described in KB 2760625 and you can download it here.