I guess I have an answer to my question. When tech support stops responding to emails about an open service request, you should complain on a public forum like this and hope that gets somebody's attention. After I posted this question, I got a private message from "Dell Cares". They directed my issue to somebody who was able to help me. Dell says they are sending me the replacement computer as originally promised. I remain unhappy about how much time I have wasted trying to get this issue fixed but at least this is progress. Hopefully the replacement does not have the same problem as the original. I am disappointed that the warranty period doesn't reset given how long this has taken.  While I am glad that posting here worked for me, it seems very inefficient to ignore customers with issues and then monitor the discussion forum for the resulting complaints that need to be expedited, vs. just offering effective tech support in the first place.
I sent my XPS 8940 desktop in for service to Dell. When Dell shipped it back, the video card I paid extra for was replaced by a cheaper model. Dell promised via email to send a replacement with the correct video card. That was almost a month ago. Now I cannot get any response or update from Dell about the service request which is still open.  Phone and chat support have been useless. I finally managed to get in email communication with Technical Support and Global Commercial Exchange Operations but they are no longer responding to emails and have not for several weeks. What other option do I have to contact somebody that can help me? 
Nobody will give me an update about a month-old open service request - who else 
can I contact?