I don't get it. Why did you jump to the conclusion that your GPU is dead when it still works on BIOS/POST.
Here's an super advanced level logical analysis,
BIOS + 7770 = Works
BIOS + Built in GPU = Works
Windows + 7770 = Doesn't Work
Windows + Built in GPU = Works
Above, all 4 of the components in this analysis works on at least one of the combinations, so all 4 of them are OK, none of them are dead. Just a single combination doesn't work, but again both components on this combination works on other conditions. Then, there must be a problem on the factors that is involved on that certain combination. And one big factor I can name, that is, the Windows 10 drivers.
OK, lectures aside, try out a different version of windows, or try to run a Linux from pendrive to make sure of what I'm suggesting, that is the GPU is not dead, before trying to put it into an oven. But if you really actually want to just upgrade the GPU, and really want the current one to die to make a path for that, you can donate it to me for free.
