FWIW, I work for a company that buys a lot of Dell, and we have had an entire machine replaced in the past...but they are certainly reluctant to do it, if they still do it at all. I had an issue with a rackmount workstation a couple months ago that took almost four weeks to resolve (and they didn't replace the machine, per se, but they replaced almost every component when it was done, except the HDDs & chassis). I requested that they replace the whole machine and they wouldn't (but it was an older machine, maybe 4.5 years, but still in-warranty).
I recently had another support request (for a week-old rackmount workstation), and I insisted that they send ALL of the potential "problem components" & have the tech replace them all at once so they didn't waste another three weeks of my company's time. Dell obliged & the workstation was up-and-running the next day after the tech swapped the parts.
BTW, sorry to hear of your experience with this machine & hope they'll resolve it to your satisfaction. Make some noise to the support team if you aren't satisfied...someone follows up with me on every case I submit (usually the day after it's closed by the tech) & they've taken care of post-service issues for me (although not always immediately, as evidenced by the first story in my post).