laptop is supposed to work between 3 cell lipo voltage and whatever the charger voltage is. don't place too much emphasis on the power supply
it has to be good for sure, but it's definitely not critical.
check the voltages - go from charger input , check B+ rail - that's your combined rail supplying the whole laptop (either coming from charger sitting at around 19V or coming from battery and is much lower ). if B+ is not present check eround teh BQ circuit PU301 in the schematic. if B+ present then check the 3V LDO - it's in PU904 , this a is a voltage which powers the KBC (keyboard controller) which in turn is responsible to enable the always on rails - (signal EC_ON to PU904 and PU905) if it reacts to power on then check your always-on voltages +3VALW and +5VALW if those are present and it's not powering on then it might be some other supply rails are missing or shorted (check further by schematic) or you might be having a "rotten" bios.