So I did all you said and sadly no picture out the external display with the 780m, no heatsink etc. The seller stated DELL/Alienware.
I'm leaning towards a dead card now as I put the 6970M 2GB back in and have display out the external monitor.
Just to clarify, I should have external display with the 780m regardless of bios if it's set to boot to Windows correct?
I'm not sure... since you have the orig gpu, i would install High Sierra, that should boot just fine with a 780m(without boot screen of course) and one of the external monitors will work(if i remember correctly the displayport closest to the usb). Its possible that the card has a bios that is not compatible(before we had the custom bios, people reported this and flashing with a different dell bios from techpowerup fixed it). So i would suggest trying High Sierra. If it doesn't work, i would try with Nick's bios by flashing with an USB programmer and soic clip. Make a backup of the bios that is currently installed, update it. If its still nothing, the card is most likely dead, so i would flash the original bios back ask for a refund.
If you shorted something with the heatsink or bracket, the system just won't boot based on my experience, but the card would still work after the short is gone.