Kindly provide FULL PC specs, including the make/model of your PSU and Motherboard. DO you have the latest BIOS installed on your PC ? Clear and rest the CMOS settings, if need be.
If you can't get a connection with the GPU, then first you need to boot your system via motherboard's Integrated Graphics Processor/onboard graphics.
Remove the card, if possible, and then plug the Monitor's cable (HDMI, DVI) to the igpu/onboard graphics. After doing this, your system should boot properly. Let me know, if it doesn't. After booting in Windows, you can check the current BIOS version installed on your PC.
But MOST importantly, did you properly connect the PCI-E cables to the GPU from your power supply, 6 and 8-PIN PEG connectors, as applicable ?
So, even if you boot the system via the iGPU, there is no signal, and the screen stays black ?
If you have connected the Monitor's cable to the iGPU, then it's n not necessary to remove the GPU, but it would much better, if you can first physically remove the card, and then try booting via the onboard graphics.
Something might be wrong with your motherboard then, assuming you cannot even boot properly via the onboard graphics. I'm NOT fully sure though. Clear and reset the CMOS/BIOS settings, if need be.
Looks like something might be wrong with your current Motherboard, IMO.
When you took the other card out , was the PSU unplugged or turned of with the switch on the back? PSU's still have a little power on the motherboard even when the computer is turned off. I always make sure I am unplugged when changing components. Did you say the onboard graphics were working?