You have an extra closing </div> tag in your code that is messing things up:
Remove that and you'll be OK, except that you should also remove the height on the #searchbox div, which appears in two places:
<div id="buttonclick" style="width: 73px; height: 35px" ><img src="images/buttonclick.png" width="73px" height="35px" onclick="submitform()" style="cursor: hand" /> </div>
width: 501px; height: 37px;
The #searchbox idv is meant to wrap around the whole form, so you don't want that height set on it.
<div id="searchbox" style="
background: #fff url(images/searchbox.png) no-repeat center scroll" display="block" >
Also, the code in blue above is invalid. Just remove it, as a div displays as a block anyway.