iMac won't power on after adding HDD. No LED lights up. What broke?

I carefully took apart a 27” Retina 5K iMac, following the iFixit guide, to replace the blade SSD and add a HDD. I discovered that I couldn’t replace the blade SSD with the M.2 drive I had bought, so for now I just added an HDD cable along with an HDD.

I put the computer back together, plug in power, and nothing happens. No startup chime, no fans, no backlight, no power through USB. After some quick research, I took off the display to check the diagnostic LEDs, and none of them are lit up. In case there was a loose connection somewhere, I took the computer apart and put it back together again, but I have gotten the same result. I did notice, however, that there is a buzzing noise coming from the power supply that can only be heard when the display is removed and my ear is close to the case.

Conventional wisdom seems to be that the power supply and/or logic board need to be replaced. However, I’ve seen some people wonder if the AC inlet is to blame, and I’ve seen at least one person claim they fixed this issue by removing the hard drive they had just installed. I am going to try that, but I don’t expect it to work.

How do I go about figuring out which components are to blame? I’d rather not shell out for every component if I don’t have to.

Thanks!