|Then that leaves the graphics card, the power supply, the motherboard, or the connection from the video card to the monitor.|
Try borrowing a different power supply.
How are you connecting the monitor? If you are using a DVI to VGA adapter, does your video card support it? Not all do, and of those that do, only one of two ports support it (DVI-I vs DVI-D ports) on most cards. What ports do both your monitor and video card support in common? Have you tried a different port or at least a different cord/connector?
Have you tried installing the old driver and reinstalling the new driver before you swapped cards?
All references I see of the GTX 760 card is that it requires an 8 pin PCIe power connector.You MUST use one. See image:
You have to be a little bit crazy to keep you from going insane.