DOA Latitude -- and no one at Dell will help me

Bought a Latitude 7370 with accidental damage coverage and additional years of warranty.  Computer arrived totally DOA, charger worked but laptop wouldn't power up.

After multiple incredibly frustrating interactions -- including emailing support and receiving no answer back within a week, calling support twice and being hung up on, sent to three different departments (two of them twice each, by reps who ignored my protest that this was the exact department that had sent me to them!), and chat reps who straight-up lied to get me out of chat and said I should just contact Dell Consumer order support, who of course told me they could do nothing and I needed to phone SMB support, which I couldn't because they close at 7 PM -- I finally, after DAYS, managed to get an order support rep on the phone who apologized, promised to replace my system, and said I would receive an email from the returns and replacements department within 1 business day.

Well, it's now been 3 business days.  The support request number I was given after the most recent phone interaction goes to a black hole, no activity is associated with it.  Am I living in the Twilight Zone?  Do I have any alternative besides initiating chargeback procedures with my bank?