Soldiering will not help a lot in cases of dead GPUs. Now, few things:
# If you tested this GPU on multiple computers that have working PCIex slot, and it shows no signs of life, its probably dead.
# You tried other cards on your computer - no image; now that is a bit confusing. Maybe you did not change your BIOS to initialize PCIEx GPU instead of using onboard? Depending on your motherboard, there should be a BIOS setting that prioritizes discrete GPU instead of onboard. If this is not what is causing it, than I suspect power supply. Even if something is wrong with PCIEx slot, your graphic card shouldn’t get fried by that. On the other hand, faulty power supply can fry both GPU and PCIEx slot. And in some even more bizarre cases monitors that are not plugged into a grounded socket can fry graphic card, and other components (this was more common with VGA/DVI ports).
It is fair to assume your graphic card is dead. As a last light of hope, you could try updating your MBO BIOS to see if thats gonna change anything, but chances are slim.