I got a different replacement S7 board. After it worked fine for a day in all sorts of tests, after a week of vacation, it suddenly had difficulty to power off and then would not power on at all. It worked again, then acted dead once more. Sounds familiar?
So I changed the PSU. I noted my workbench power button cable had a side broken. Replaced that. Then it powered on reliably again. Then I thought: I only used a different PSU briefly with that broken button. Then I went back to the original PSU. Which caused the same trouble again, after working fine for some time. Perhaps...
And yes, with a different PSU, my old beloved SS7 board powers up again. 😀
So I have a faulty PSU to diagnose. It doesn't start up every once in a while... Good trade!
Retro PC warning: The things you own end up owning you.