What is your PowerMac G5 model specifically off the machine's labels?

Is it a Dual Processor (DP), Dual Core (DC) or some other variant, as the ASD CDs do require the correct disc version to test the hardware.

Having said that, if the machine is running OK, then almost certainly all the hardware is working as it should.

If you have a Dual Processor PowerMac G5 then sometimes, and it has happened to me, that one of the CPUs can fail, but swapping the working CPU to the first slot can make a non-starting PowerMac ignore the failed CPU and start OK.

Ideally you'd need to acquire a working CPU to replace the failed one, but you can manage with just the one working CPU with MorphOS, as it only uses one CPU anyway currently.