This happens when you have un-closed HTML tags in the slider or in the page which messes up everything on this page including the SEARCH.

The easiest way to find out where is the broken code is by removing the code of different parts of the page. Start form the sub-footer, followed by top header then the page content. If removing the code fixes the search then you have a winner. 

Next step is to fix the code itself or start from scratch.