I found the fix! Play with it long enough and it usually works out.

The following code works for vb.org:
PHP Code:
<form action="https://vborg.vbsupport.ru/search.php" method="post" name="vbform" target="_blank">
<input type="hidden" name="s" value="$session[sessionhash]">
<input type="hidden" name="forumchoice" value="-1">
<input type="hidden" name="action" value="simplesearch">
<input type="hidden" name="searchdate" value="-1">
<tr class="secondalt">
<td><a href="http://www.vbulletin.org/" target="_blank">vBulletin.org Search</td>
<td><input type="text" size="30" class="bginput" name="query" tabindex="1"> <span id="submitrow"><input type="submit" class="bginput" name="submit" value="vB.org" accesskey="s"></span></td>
</tr>
</form>