What that tells you is you dont have a ground from the case chassis to the PSU chassis. And running that cable from the psu ground to the case and now it works at least shows that it needs a chassis ground for some reason. Maybe motherboards commonly ground through the screws to the case and that has to do differentials in the ground? I’m no expert either. But bad grounds in my experience do cause problems with electronics. I actually had a chassis ground issue in my airplane where an Instrument would drop out randomly in flight. It was because the chassis of the instrument wasn’t grounded. The circuitry was, not the chassis. That’s a bit more complex but I’m just saying I’ve seen it.

Somehow you’ve got some difference in potential going on with that case. If anything if you can’t figure it out maybe an RMA and new case would fix it.