What theme are you using?
You may be able to remove the search button by editing the CSS file. Try inspecting your site to locate the DIV element that is associated with the search button. Once you locate it you should be able to add “display:none” in the Custom CSS to remove the search button. If you ever decide you need the button back, you can simply remove the text you added.
Theme is a child them of Twenty Eleven.
How do you inspect the elements? I’ve tried to put additional CSS codes to remove it in the Simple Custom CSS and Additional CSS areas, with no positive results
Most of the common web browsers offer an inspect elements option. Most commonly this is accessed by right clicking on your web page and selecting the “Inspect Element” option. This will open a window pane that will show the website HTML and CSS. As you hover over the items in the inspect pane, it will highlight the portions of the web page connected to that element.
See the following link for additional information for the major browsers.
https://en.support.wordpress.com/custom-design/how-to-find-your-themes-css/