hi,
usually the supervisor IC test the outputs from shorts and if it's ok, he 'validates' the 19V
check all regulators from short and eliminate if you can
or just 'validate' yourself the 19V after identifying the correct mosfet and connecting D-S directly, the other one is for discharging.
if you find some voltage with short circuit, just inject that voltage from a good and powerful supply (that means something like 8A current capability, that's what it takes to burn a shorted capacitor) after disabling eventually the voltage regulator of your mobo.you're gonna have the surprise to see the damaged part popping up in 2 seconds.
seems risky, it's not, I've done it in a repair shop on lots of mobos with almost 100% success rate
sometimes I just bypassed the mosfet who validates the main supply and all came to life.but usually it was a short involved on some supply rail.in rare cases an regulator IC was to be replaced, but with some ic's this is not impossible.
study the datasheet of each regulator for good understanding on where you can inject the voltage and how to cut the regulator output on mobo
yes, it takes time.but 120 euros mobo also takes time...
regards,pierre
ps:
apparently it's not 19V validation issue, more a shorted small voltage power rail (you said you have some of the smaller voltages present).Identify which voltage is it, apply coresponding voltage, find shorted cap.finding the voltage it's not so complicated, trace the rail to the 'consumer' IC/module and then, that's your voltage (it depends on your finding, but not really complicated, may be prcessor or usb or whatever)