Don't modify core files!
Magento adds the history tab in sales.xml
as follows:
<customer_account>
<reference name="customer_account_navigation">
<action method="addLink" translate="label" module="sales"><name>orders</name><path>sales/order/history/</path><label>My Orders</label></action>
</reference>
</customer_account>
You can use the same layout update in a custom module:
<customer_account>
<reference name="customer_account_navigation">
<action method="addLink" translate="label" module="your_module"><name>unpaid_history</name><path>your/controller/unpaidHistory/</path><label>Unpaid History</label></action>
</reference>
</customer_account>
This will add a link "Unpaid History" pointing to your/controller/unpaidHistory
For the layout of your custom controller, you can look again, how Magento does it with the history:
<sales_order_history translate="label">
<label>Customer My Account Order History</label>
<update handle="customer_account"/>
<reference name="my.account.wrapper">
<block type="sales/order_history" name="sales.order.history">
<block type="core/text_list" name="sales.order.history.info" as="info" translate="label">
<label>Order History Info</label>
</block>
</block>
<block type="customer/account_dashboard" name="customer.account.link.back" template="customer/account/link/back.phtml"/>
</reference>
</sales_order_history>
Copy it to your layout file, replace sales_order_history
with your_controller_unpaidHistory
and replace the <block type="sales/order_history">
block with your custom block and custom template.