A1347 Mac mini won’t turn on

Sorry for stating the obvious but it's not clear if you've tried resetting the SMC per Apple:

(Mini without T2 chip; other models at link)

"Desktop computer

If your Mac isn't a laptop computer, follow these steps:

1. Shut down your Mac, then unplug the power cord.
2. Wait 15 seconds, then plug the power cord back in.
3. Wait 5 seconds, then press the power button to turn on your Mac."

Reset the SMC of your Mac - Apple Support

Or if you've tried directly plugging into a different mains outlet on the same and different line feed.

If no joy, try lightly cleaning with alcohol the power plug's and Mini's connection points. Completely air dry before reconnecting.

Good luck.

That machine is obsolete and no longer supported. You dispose it off for free at any Apple Store. Then replace with new.