These may seem like very basic, why is he asking these, but I’m not there, you are and i’m trying to get a complete picture.
If everything works with two gpu’s and you add the third and then the system will not even boot/ power up? yes or no
When you hit the power button are there any beeps from the motherboard stating that it cleared posting? yes or no
No screen showing on the monitor? yes or no
Its booting, but seems to hang/stuck and after a couple minutes I just turn it off ? yes or no
Have you removed one of the gpu’s and placed the 3rd in its place to make sure it works? yes or no ?
Have you tried different power cables from the psu to the gpu?
Is your PSU new or used?
Do you have a wattmeter to see how much you are pulling from the wall?
IMO what you describe sounds like you have a ground short when you connect the 3rd gpu, what is causing this I’m not sure