How did you verify it was only your previous motherboard that bit the dust? I would consider the graphics card to be suspect after coming out of a computer that developed a defective motherboard.
Switching to a new motherboard of the same make / model can present differences in equipment. You should start by making sure you have the same UEFI / BIOS on the new board, or possibly newer if there were improvements, as it was working for your equipment on the last motherboard. Second, you need to go through the new board's UEFI / BIOS settings pages and configure it as your old one was configured, or at least to the best of your recollection.
Pay attention to the part in there about booting UEFI add-in cards. If your GPU doesn't have a GOP section in it's BIOS, it's not going to be compatible with a pure UEFI boot, but I am under the impression that a GTX 760 should support UEFI boot. You should also try the legacy boot option for your motherboard, just in case, as we don't know the required setting for a generic, unspecified GTX 760.
Was the replacement 1155 motherboard new or 2nd hand? Perhaps the slot is defective? Try the bottom x16 slot on the motherboard.
Make sure the graphics card is fully seated in the board with the clip locked in place to secure the card-edge connector.
Do you have another graphics card laying around you can test in the system? Just a quick swap with a power on should tell you whether add-in graphics are going to work at all. You shouldn't need to boot all the way into Windows, as getting into BIOS with an add-in board is sufficient to determine your system boots fine with a discrete graphics card.
What about the power supply? Is there any reason to suspect the power supply could be problematic at this point? A GTX 760 is going to require significantly more power to run than your integrated graphics on the CPU. You haven't actually explained the reason for the failure of the motherboard, so that still leaves questions.