You can certainly do this, however, you will need to alter the SQL statement which pulls these orders into the admin index page.
For this, open admin/index.php of a zen1.3.8 install, and go to line 165 to find this code:
<?php $orders = $db->Execute("select o.orders_id as orders_id, o.customers_name as customers_name, o.customers_id, o.date_purchased as date_purchased, o.currency, o.currency_value, ot.class, ot.text as order_total from " . TABLE_ORDERS . " o left join " . TABLE_ORDERS_TOTAL . " ot on (o.orders_id = ot.orders_id) where class = 'ot_total' order by orders_id DESC limit 5");
You now need to edit this sql statement so that it only pulls in the specific orders you need. So check your order status values, which can be found under Localization >> Order Status. As standard Delivered is order status 3, which is shown in the URL when you click on Delivered in this screen. So now you can do one of two things. You can either show all orders not delivered, or you can show orders which are placed, or pending.
So backup this file, and then replace the line above with the following:
Not Delivered:
<?php $orders = $db->Execute("select o.orders_id as orders_id, o.customers_name as customers_name, o.customers_id, o.date_purchased as date_purchased, o.currency, o.currency_value, ot.class, ot.text as order_total from " . TABLE_ORDERS . " o left join " . TABLE_ORDERS_TOTAL . " ot on (o.orders_id = ot.orders_id) where ot.class = 'ot_total' and o.orders_status != '3' order by orders_id DESC limit 5");
Pending Or Processing
<?php $orders = $db->Execute("select o.orders_id as orders_id, o.customers_name as customers_name, o.customers_id, o.date_purchased as date_purchased, o.currency, o.currency_value, ot.class, ot.text as order_total from " . TABLE_ORDERS . " o left join " . TABLE_ORDERS_TOTAL . " ot on (o.orders_id = ot.orders_id) where ot.class = 'ot_total' and (o.orders_status = '1' or o.orders_status = '2') order by orders_id DESC limit 5");
This code may need a little tweak to suit your exact setup, but you get the idea.
Good luck,
Absolute