I had this same issue and took the whole system apart including reseating the CPU and even flashing the BIOS again directly on the chip.

Finally going through the service manual again we found a section on the "Battery" 

No not the CMOS battery but another battery in the system which it doesn't describe what it's purpose is.

It's incased in a black plastic box which holds the 2 AA batteries located by the hard drives.

It's connection goes to the front panel with the USB connections.

Replacing the AA batteries fixed the no POST and booted right into the BIOS. Since we had flashed it and it popped up with CMOS changes needing to be updated.

Set all the drive info and and UEFI type and the system booted back up like normal.

Hope this helps anyone with the no POST issue as i've seen many threads on the internet with people having the same issues.

@BMAN549​ Thanks for the tip about the 2 AA batteries. Didn't fix the issue, but at least I cleaned out the leaked old batteries and put in new ones. Looks like these AA batteries are backup for the LED light inside the case.

Figured there was some kind of a catch. I’ll look into that! Thank you.

I'm pretty sure the Windows Operating System is keyed to a specific motherboard . . . so you can't just throw in another hard drive. You will have to purchase a new Windows software and key.

The software they offer to recover requires getting into the bios screen, they computer doesn’t even show a splash screen. I’m unsure if that will work.

A working computer should be able to Post, show-BIOS options. Most Dell/Alienware can even run ePSA Diagnostics . 

Try F12 on-boot. A working Area51-R2 should be able to boot the following flash-drives ... Microsoft Windows-10 Installer, Macrium Rescue, and Ubuntu Linux .

From my Area-51 R5 experience, if there is a single 3rd party fan installed, the system will boot into an infinite loop of diagnostic fail, with constant black screen on the monitor. I had to add 3 OEM Nidec fans with Y-splitter adapter cables to get a successful POST.

You seem to have a no video no POST situation.  When you trade for it did the previous owner demo it was working right before switching ownership?  If they just claimed it was all working without you verifying that could be a problem.

In a no POST situation try remove all memory and all connected storage devices and all peripheral devices such as usb keyboard etc.  Install only one ram in dimm 1, use a very simple video card that was verified working on another pc to test.

R2 board has a proprietary 8 pin gpu power connector socket at lower right corner.  confirm Dell psu is plugged in that socket.  not sure board would post without this connected even when you are using a low power gpu.

Honestly that part of the trade was just icing on the cake on my end so I was not too worried about it but I really like how it looks and now I want to use it.

I’ll check for that plug at the bottom, I have removed all GPU’s and tested with working card. Still nothing.  

The 3 fans in it all seem to be OEM. Has the stock liquid cooler as well.