A1347 2010-2012 common issues
Tantalum Polymer Capacitors on the 5V rails can become short. These capacitors are for USB 5v line. if they become short then the mac mini will not turn on.
remember capacitors polarity. check the green circled caps for short.
the value of the cap is 150UF, 6.3v, Case B2. https://uk.farnell.com/panasonic/6tpg150mzg/cap-150uf-6-3v-tant-polymer/dp/2982731