Look here
https://learn.sparkfun.com/tutorials...suring-voltage
http://www.ianstedman.co.uk/Amiga/am....html#cd32lead find the picture of CD32 pinout.
Plug psu in to mains. Take the black lead of your multimeter to the GND pin and the Red lead to 5v pin. Read voltage from multimeter screen. Do the same for the 12v pin.
I know you said nothing on screen, but do you mean absolutely nothing? Is there even a change in black levels?
Do you have an Amiga mouse? Try it in port 2 of the CD32. Press and hold both mouse buttons whilst powering on CD32. Can you enter early start menu?