Few days back I was working on a theme design and faced a very rare issue. The issue we faced was magento search not working in Magento Responsive Magento Web Design theme which is by default provided with the bundle of magento.
I took few steps to make it working and found out many solutions which can work for you.
Here are few steps you should take and check before you make a final call to change the coding:-
Clear Magento cache
Sometimes due to caching issues in magento the search might not work so to solve this problem the preferable solution is to flush magento cache.
To flush your magento cache all you have to do is:-
Log in to your magento admin and go to System -> Cache Management and then flush your magento cache
If you are in development mode you can disable the cache if you want to by just selecting all and then selecting disable from the actions dropdown.
Sometimes if magento is not indexed properly then also there can be issues in the search. So another suggested and solution is to reindex the data in magento.
To reindex your data all you have to do is :-
In your magento admin panel you have to go to System -> Index Management in that click on select all and then select Reindex Data from drop down and then submit.
Return to base magento theme:-
Get back to base magento theme and check if the magento search is working or not if its working then there must be an issue with the themes custom coding .
If it’s working compare files named catalogsearch.xml
Now where is catalogsearch.xml file :-
Compare the file in app/design/frontend/base/default/layout/catalogsearch.xml to app/design/frontend/default/your_theme/layout/catalogsearch.xml and see if you are missing any line of code.
One more thing you can do to test is to take a backup of catalogsearch.xml of your theme and delete it from the directory to see if it is working.
Check product attributes:-
Sometimes due to some reason attributes are not properly configured.
To manage your attributes go to catalog -> Attributes -> Manage attributes Seach for name attribute And configure it like we have (Important check that the scope of name attribute is set to Global).
Also search for sku attribute And configure it like we have (Important check that the scope of sku attribute is set to Global).
Change the configurations of search:-
Sometimes the configurations of catalog search are not properly defined.
So to change the search configurations we have to go to System -> Configuration on the left hand side click on catalog and from that select catalog search tab and configure it like we have done.
I hope this is able to solve your problem. If still your magento search is not working, kindly let me know and i will help you out.