You installed the K3100m, did you install and setup a bootable OpenCore thumbdrive (with your OS choice) before you put the new graphics card in?
The steps i've used are as follows:
Upgrade the imac to at least High Sierra and build two bootable USB thumbdrives, #1 to boot the imac with linux headless to flash the GPU when you replace it, and #2 with the latest OpenCore installed and configured for your imac.
Then replace the CPU/GPU. Put it back together but leave the screen off (so you can see the leds) AND leave any internal HDD/SSD power unplugged. Plug the linux USB drive in and plug the power in, you should have 1 green light, turn it on and you get 2 green lights, the chime and it'll boot from the linux USB. I am assuming you have the imac ethernet plugged in and know how to get your ip address so, yes, from your windows box you SSH into the imac and flash the new GPU. After the GPU is flashed, shutdown and install the screen. Plug in the bootable OpenCore USB, power it on and you should see the boot selector screen. If not (the screen is blank) then power off, power on doing a Pram reset (chime twice) and see if the boot selector comes on. If still no screen repeat the pram reset. If still no boot selector then you've built the OpenCore incorrectly and you need to use another imac or macbook to rebuild OpenCore for this machine. If you still have a black screen then fallback to the linux USB, remote login and reflash it a second time. You should get a message about the flash image is the same, then you know the card has the firmware on it. Finally, after you get a boot selector, power it off and connect the HDD/SSD power but leave the bootable OpenCore USB drive plugged in. It's important you NOT have the HDD/SSD plugged in previously because otherwise the imac will default boot from that first, never the USB drive, and the screen will not come on without OpenCore installed.
I've done this several times, 2010/2011 21.5 and 27" imacs. When you get boot selector your ready to install the new OS. Sometimes I'll need to hit the spacebar at this point and boot into Recovery mode or clear nvram, but if you get boot selector your golden.
Hope that helps.