an ATX power supply won't turn on just sitting on the table with nothing connected to it. you have to cheat it by bridging pins 16 (PS-ON) and any ground - the closest is right above it on pin 15 or below on pin 17. even a piece of solder will do, it's just a logic signal and doesn't carry any proper electricity.
I am pleased to report that the PSU is perfectly healthy. all the voltages were as expected. it's a PSU from a brand I hadn't heard of from 2013, so I wasn't really expecting that haha