OK soI begun to try to help myself but I still need help...
I found that I needed to modify
after line 557
$prodRow .= '<td class="prdPL"><div><a href="' . zen_href_link($handler_page, 'products_id=' . $products_id) . '" target="_blank">' . $cats[$cat_index][$prod_index]['products_name'] . '</a></div></td>' . "\n";
and it works, it adds the product showing the cart in a new window or a new tab (depends how your browser is configured).
$display_qty = (($flag_show_product_info_in_cart_qty == 1 and $_SESSION['cart']->in_cart($products_id)) ? '<p>' . PRODUCTS_ORDER_QTY_TEXT_IN_CART . $_SESSION['cart']->get_quantity($products_id) . '</p>' : '');
// show the quantity box
$prodRow .='<td>' . zen_draw_form('cart_quantity', zen_href_link(zen_get_info_page($products_id), zen_get_all_get_params(array('action')) . 'action=add_product'), 'post', 'enctype="multipart/form-data" . " target="_Cartpage"') . "\n" . $the_button = PRODUCTS_ORDER_QTY_TEXT . '<input type="text" name="cart_quantity" value="' . (zen_get_buy_now_qty($products_id)) . '" maxlength="6" size="4" /><br />' . zen_get_products_quantity_min_units_display((int)$products_id) . '<br />' . zen_draw_hidden_field('products_id', (int)$products_id) . zen_image_submit(BUTTON_IMAGE_IN_CART, BUTTON_IN_CART_ALT). '</form></td>';
BUT, don't think I'm a PHP guru, I don't know anything about PHP, I just played with copy/paste and many trials to get to the result.
So I would like a PHP guru to be kind enough to take a look at these few lines, and correct them to make it clean PHP syntax and clean regarding the zen guidelines.