HOW LONG DOES IT TAKE TO ENTER A SERVICE TAG? I'VE CALLED 3 TIMES NOW

I ordered a PC on 12/9 and it arrived on 12/12.  The invoice with the order did not include the service tag on it (I ordered 2 PCs since and both had the service tag printed on the invoice).   

Apparently my service tag is not entered in whatever database DELL uses.   How the PC could be shipped and not entered as a valid Service Tag is something DELL should really figure out.  

The DELL support site requires a valid service tag before you can get any support so I was forced to call the phone support number.

I called on 12/24 (Support request 922078142), was transferred 3 times, was on the phone for over 30mins and was finally transferred to a number where I received the message " the department you called is closed " and it just hung up on me.  This service request still shows OPEN status.

I called on 12/31 (Support request 922311880), was on the phone for another 30 minutes, was assured that the agent would get back to me by the end of the day via phone or email.  I have received nothing.  This service request shows no status on the My Support Request site.

I called again this morning, they checked and said "Your request was only initiated on 12/31", at the end of my patience and just requested to initiate a return of this PC since I can't get any support on the PC and Dell can't figure it out since 12/9 when they shipped the thing.   Once again I was transferred to some department and received the curt message "Call back in the Next Business Day, Goodbye". 

How long does it take to enter a Service Tag?

How could a PC be shipped without entering a Service Tag?

How could "customer support" continually transfer an already irritated customer to numbers where you are just hung up on?

What are the CST hours for DELL RETURNS DEPARTMENT - I AM DONE!!!