Tested the CS-Cart check out function, everything went well when I placed a order myself. And I also received an email from the system with the order information. But the email I used as the orders department did not receive the order notification from CS-Cart.
I spent (and wasted) a lot of time to do the trouble shooting on the issue above. Even I contacted the host provider to see if the email system blocked the emails generated from the CS-Cart code. But the solution actually was simply as the below.
Go to the back-end admin control panel of CS-Cart, click the “Orders” top menu item and then “Order Statuses“. On the new page, click “Edit” or click the “Open” status directly, and check the “Notify orders department” on the next Open Status page.
That is it.