hello, please try the following steps in order to restore the search function on the default homepage:

1. go to firefox > help > troubleshooting information and click on profile folder/show folder. a windows explorer window should open up - in there delete the file named chromeappsstore.sqlite.
2. then enter about:config into the firefox location bar (confirm the info message in case it shows up) & search for the preference named browser.startup.homepage_override.mstone - right-click and reset that entry to the default value.
3. restart firefox

Which search button? The one on the default about:home homepage?