Should the unit have an extended optional AppleCare agreement in place
the option to schedule an appointment with Authorized Apple Service or
have the unit inspected first by someone who knows what to check, is an
advisement to consider, if nothing else for a referral to resolve this issue.
Sounds as though some non-conductive materials have failed to insulate
the powered sections of the internal circuitry from the outer metal case.
And so you would be able to feel any power leakage, as you would be
supplying the ground-effect or a 'conduit to ground' in that situation...
IF you wanted to see how the construct of that model Apple Mac Mini
may be affected by component failure, either look into a 'take-apart' or
an online repair guide (ifixit has both, free to view & use). Components
are modules which could be removed and replaced, carefully & in kind.
And have the grid power source checked where Mini is in use.
Good luck & happy computing! 🙂