They'll have a spare PSU to swap in as a test. Yes you can buy a Volt Meter and PSU tester but that's as much as a new PSU.

I understand you don't want to randomly buy parts but is it worth investing in the test gear?

I'm not there to work this but the usual is found with google like this: "The Dead PC."
You pull it out on cardboard and start with just two parts and work your way up.