It is possible your 'new' PSU is many years old and sat on a shelf and it never worked. You say the GPU works with an older power supply, but you mention 4-pin power, which would not apply to any recent GPU (like over a decade). You did not respond to my comment regarding that so it is not clear what your old setup was like and under what circumstances the GPU works.
With what I know so far, either you have purchased a bad PSU, or you are connecting an EPS 12V 8pin or 4+4 pin connector to the 8-pin PCIe GPU connector which should be a 6+2 pin cable coming off the Cooler Master unit. EPS connectors are the ones that plug in near the CPU. But I also don't know what CPU or motherboard you have.
Does the system work with the new PSU but without the GPU installed?