After calling 6 more times they claim they're going to do something.
I originally contacted Dell Technical support on February 06, 2016. I was told by the tech that the problem I have having with the GPU meant it had to be returned for repair. After over 5 weeks of being passed around between different support groups and filling in many different warranty transfer forms (I bought the XPS 15 9550 system in question from the Microsoft Store and at the time it was about 2 months old). I'm now stuck entirely. I was told the last rep I talked to (who is on some sort of escalation team) that the warranty is now transferred and I would have to call back the tech support number. Which I did, just to be told that they can't possibly do anything and that I must contact back the rep who told me to call them. I emailed the rep who told me to contact tech support again and he hasn't responded to me.  So right now I'm totally stuck, no one can help me and I have a broken computer that I've now had sitting here for nearly 6 weeks and I'm afraid to use it because I don't know what might happen. 
Being Given the Run Around by Technical Support