[Victor D]

Your skin is customized so I'm not sure if it helps
the common solution is to create a new file in skin1/customer with name for example menu_search.tpl
and paste into it

{capture name=menu}
<form method="post" action="search.php" name="productsearchform">
<input type="hidden" name="simple_search" value="Y" />
<input type="hidden" name="mode" value="search" />
<input type="hidden" name="posted_data[by_title]" value="Y" />
<input type="hidden" name="posted_data[by_shortdescr]" value="Y" />
<input type="hidden" name="posted_data[by_fulldescr]" value="Y" />
<input type="hidden" name="posted_data[by_sku]" value="Y" />
<input type="hidden" name="posted_data[including]" value="all" />
<table cellpadding="0" cellspacing="0"  width="100%">
<tr>
<td valign="middle" style="padding:0px;" align="right" width="100%"><input type="text" name="posted_data[substring]"  value="{$search_prefilled.substring|escape}" /></td>
    <td valign="middle" style="padding-left:3px;" >
<table cellspacing="0" cellpadding="0" onclick="javascript: document.productsearchform.submit();">
    <tbody>
        <tr>
          <td style="padding:0px;"><a href="javascript: document.productsearchform.submit();">{include file="buttons/go.tpl"}</a></td>
       </tr>
    </tbody>
</table>
    </td>
</tr>
</table>
<a href="search.php" style="background:none;padding-left:0px" ><u>{$lng.lbl_advanced_search}</u></a>
</form>
{/capture}
{include file="menu.tpl"  menu_title=$lng.lbl_search menu_content=$smarty.capture.menu}

then find in your customer/home.tpl

{include file="customer/menu_cart.tpl" }
<br />

and insert right after it

{include file="customer/menu_search.tpl" }

I need your skin1/head.tpl to find how to remove existing searchbox