Yours is 21.5" so power is a bit tight. However, your setup should work. I had a i7-2600 in a 21.5" myself, no issues.I just bought a 2600 i7 for my mid 2011 iMac based on your feedback and image comes up during boot and then goes black once finishes loading, seems like the CPU is taking down the GPU, the computer finishes loading but no image. I have an AMD WX4150 video card Wich I checked that has same TGP value than your K1100m (45W) and I also have one SSD installed, disconnected the DVD an I still get low power, what you'd you think I'm missing? I put back the i5 and everything goes fine so it's definitely the i7 sucking up the power ? any help will be appreciated thanks!
If you say it works with the i5, I assume you have all necessary patches for your new GPU so that you won't get a black screen? Bootloader/Opencore etc? So you have swapped your i7 back to i5 and no black screen, or did you have the i5 working, then swapped to i7 and it is not working?
If the latter, maybe heat sink not properly applied, chip not mounted correctly, RAM issue, GPU not plugged in correctly...
Maybe try a linux live USB stick, boot from there and see whether it is running?
It could also be something withthe GPU. Check the GPU thread for your specific card.