Well first step of any Amiga troubleshooting is to look at that powerled. of some reason this is always skipped as they watch on the SCREEN!.
among the very first things kickstart does it to turn the powerled HIGH, all amigas (with exception of A1000 and Rev 3 a500) starts with powerled on HALF brightness. So. it shlud go to full brightness after aprox 1 sec. if this doesn't happen, you either have bad kickstartroms or something that stops the machine to execute the kickstart. this is usually the hardest things to find.
then you can use my diagrom to test more stuff like bad IRQ och CIA timers, this will also make the amiga to give "black screen" etc. and USUALLY 99 times of 100 diagrom only starts IF that damn powerled goes full bright.
so CHECK THAT LED for hint on where to start the troubleshooting. if it DOES go high! your PSU IS fine. meaning it atleast deliver 5V (and 12?) it also means that your kickstart most likly IS ok. (as it can execute the code)