Now put the gpu from the other machine into the new machine.
If that does not work I'll guess it's not the gpu.
It would seem the monitor functions.
You swapped the psu so let's rule that out.
Start unplugging stuff.
You don't need a keyboard/mouse/ssd/hdd/other.
Use one stick of ram.
I built my second gaming of, and it boots up just fine. I connected it to my monitor, and no signal. I used my other computer and connected it up to the monitor to make sure the monitor works, and I got a signal. I put the graphics card in the other computer and then it works. At first, I thought it was the power supply, so I swapped it out with another one, and it still shows no signal. I don't know what's going on, and what's weird is that the fans are spinning on the gpu. If you want the system specs:
Biostar TA 970
Gigabyte windforce gtx 750ti
80GB Intel 320 series ssd
1TB Toshiba hard drive
Corsair CX500 power supply
8 GB ddr3 ram