Non-Inventory Item does not appear in the list of Items when entering a Sales Order from the Customer Center

To be able to make the Non-Inventory Item show in the Customer Center as the customer creates a Sales Order, there are 3 essential points to make sure:

1- The item type is NOT For Purchase,
2- The Display in Web Store checkbox is marked under the WebStore subtab in the Item record,
3- A Base Price is defined under Sales/Pricing subtab in the Item record.