Actually, I noticed that basically the whole page is clickable, not only search box. It seems there is an onclick function in the header that is "leaking" out over the rest of the page.
Here's that section:
<div id="header" onclick="location.href='http://www.nevis1.com/nevis1blog/';" style="cursor: pointer;">
<div class="header">
<h1><a class="blog-name" href="http://www.nevis1.com/nevis1blog">Nevis, West Indies. “A Non-Tourist-Trap” Blog About Nevis.</a></h1>
<h2 class="blog-description"></h2>
</div>
I see no definition for the id "header" in your stylesheet, only a class, and the div is open. I suggest you try replacing the above with the following:
<div class="header" onclick="location.href='http://www.nevis1.com/nevis1blog/';" style="cursor: pointer;">
<h1><a class="blog-name" href="http://www.nevis1.com/nevis1blog">Nevis, West Indies. “A Non-Tourist-Trap” Blog About Nevis.</a></h1>
<h2 class="blog-description"></h2>
</div>
That removes the redundant div, and moves the onclick funtion into the real header. And the code would most likely be found in header.php.