To have the "new topic" button I think you just need a link to:
$scripturl . '?action=post;'
and then to run this code:
$context['show_boards_dropdown'] = true;
require_once(SUBSDIR . '/Boards.subs.php');
$context += getBoardList(array('not_redirection' => true, 'allowed_to' => 'post_new'));
$context['boards_current_disabled'] = false;
if (!empty($board))
{
foreach ($context['categories'] as $id => $values)
if (isset($values['boards'][$board]))
{
$context['categories'][$id]['boards'][$board]['selected'] = true;
break;
}
}
somewhere while loading the post page, that should load the select for picking the board.