Creating a Views Search Page AND Block (not just a search block and results page)
Consider using a block with php filter to display the exposed search box in a block.

Example below is based on Search API with blocks exposed. I'm taking a guess you're using Search API based on your description.

For Search API:

$view = views_get_view('your_view_here');
$view->set_display('Page');
$view->init_handlers();
$exposed_form = $view->display_handler->get_plugin('exposed_form');
print $exposed_form->render_exposed_form(true);

For Drupal's Core Search:

$block = module_invoke('search', 'block_view');
print render($block['content']);