To everyone, who happen to land on this topic: I contacted DELL Support team. They said that having two cards with the same behavior shows a problem with the MoBo and that not much can be done since support period expired besides RTC Reset . So I followed the steps to do it. Turned out my machine is not designed with this functional availability, so I did BIOS reset instead. Result is that nothing happens - initial POST does not recognize either of the 2 external discrete cards I have installed at that moment. So I am stuck with the onboard integrated Intel video card for the time being.   Good Luck to all.
I see quite a number of topics regarding the disappearing of the Discrete GPU regardless of nVidia or AMD(ATI). All share common pattern every time: Laptop used as normal previous day and on the next day - bam - > no GPU visible in UEFI(BIOS) and hence no GPU 1 in Windows 10. My case is no exception. What I did was to take the Precision 7510 in certified repair shop, where nothing else was registered except that they confirmed the GPU (AMD Firepro W5170m) is installed. They did not recommend to purchase another one (I found out later why) Anyway I ordered another GPU from ebay (US based shop) and had it installed  - both cards look exactly the same. They said both cards are having a look as working - nothing visible to have been damaged. Result is that nothing has changed, so now I have a Precision Workstation 7510 with integrated graphics. and 2 AMD cards(that I think are in working order but can't prove it).   So since there are so many cases of laptops and especially Precision Workstations with not detected Discrete Graphics cards (MXM in my case), I suppose that someone has figured it out and probably a solution is around the corner.   So question is can I do anything else to get to the bottom of this?
Discrete GPU suddenly gone