Mini PC received higher voltage (19V instead of 12v) what hap
The mini PC is broken, because components inside it were exposed to a voltage higher than what they were designed for. The damaged components probably caused an internal short circuit to form, which is why your 12V adapter light goes off. It's basically impossible to guess what's broken without at least some pictures from inside the PC, but it's highly likely that the damage is not easy to repair, if it's possible at all.