I have had this problem with two 2070 Super OC Black cards. I have sent the first one back as an RMA, EVGA says that it passed their tests fine and nothing was wrong with it. Both times I have used HDMI, but I am buying an DP to HDMI adapter later today to try that. 
 
When I received my RMA in the mail, I immediately plugged it into PCIE slot 1, booted to windows fine. After restarting my PC and installing the 1070 with it connected to external power, I could boot to windows for only a short period of time, before the 2070 sent no signal to my monitor and would never work (with HDMI at least) again. The old 2070 did the same exact thing. I re-installed my old 1070, took out the 2070, updated my bios, downloaded EVGA 20x family support drivers, and reset my CMOS and BIOS. Plugged 2070 back in, same thing, blinking white cursor in top left for a second, computer power flashes twice, then I wait infinitely for nothing to happen. 
 
Oddly enough, when I boot both cards in my system (1070 connected to HDMI and powered by external psu) I can change my boot priority to boot to my linux (NicehashOS) live USB, and it detects both the 2070 and the 1070. When I leave this miner running, the 1070 has a higher hash rate (27mh/s) than my 2070 (17mh/s). 
 
How can I fix the 2070? Is it possible to reflash the 2070? Is my motherboard (IPSKL-SC) too old?
 
My setup - 
Alienware Aurora R5
i7-6700k 
650w EVGA fully modular bronze psu
32gb DDr4 
1tb toshiba hdd
 
 

willstrz2
Solved the problem. 
 
Bought a display port to HDMI adapter ($12.99 at best buy), boom, bios screen and booted straight into windows no problem. Downloaded the driver, everything working perfectly. 
 

This could be a driver bug. Have you  submitted a bug report to Nvidia? Others have reported strange issues using more than one GPU in a system.

that sounds really weird.  I was going to say that the issue may be the UEFI on the newer card having issues on the Alienware motherboard . 
I'd check for an updated BIOS to that board, while you're at it.