A wrong CPU would not cause unresponsive power supply.  The power supply may be dead as it did not response to a BIST test.  Start looking around for a good power supply for testing. Before searching for a correct power supply, you may want to check the power supply and motherboard again as they should have standard 24-pin connector for power. Here is the owner's manual for your reference.  
Hi there I recently bought a Dell Optiplex 9010 (MT) untested and went about with due diligence checking that everything was in place. I plugged in the power cable and tried switching it on but did not get anything. The power button does not work and is not illuminated at all like it would usually be (blue/orange). At the back, the power supply LED light is off and does not indicate that the PC is getting power at all. I tried pressing/pressing and holding the black button on the power supply but still nothing happened. I then decided that the power supply might be bad. The PC was advertised as an Intel 3rd Gen and when I checked the CPU later on, I found an i5-4590. Then I thought that the seller might have just made a mistake with the generation version and actually sold me a 4th Gen PC. However, I did some research and found that the PC is indeed a 2nd/3rd Gen and that the wrong CPU is installed. My main question is whether a wrong CPU would give these symptoms - that is, whether this will make the PC not be responsive at all as if it's not receiving power? I am looking for a compatible CPU in the mean time and will test further, but just wanted to be sure about the power issue before I start looking around for a different power supply. The power supply has a proprietary 8-pin main connector and not the standard 24-pin and I don't have another PC/motherboard to test the PSU on. Thank you - looking forward to your response 
Dell Optiplex 9010 won't start