The PSU has several voltages, not just one. If one rail has failed, whole system may show some signs of life but not all of it will work.
Without substituting known good working parts such as memory, CPU & PSU, I'd gamble and say the whole system (motherboard/CPU/memory)needs replacing. And if it's an older system you'll need a suitable new PSU as well.
I can't confirm that of course but I don't think it's worth spending money on individual new parts without proving existing individual parts faulty.