not turning on, battery does charge.

I got a A1502 from 2015 here with a 820-4924-A motherboard that came in for a battery change. The customer had contacted me before to replace the battery as macOS was indicating the battery needed servicing. Though, before the client was able to bring in the laptop to get the battery exchanged, the laptop stopped turning on. I already had a new battery here for him so I went ahead and installed the new battery. The battery did fully charge but the laptop still would not turn on.

Upon further examination I found that the power inductor L7630 (SPM6530T-1R0M120) had corrosion hidden by the black sticker in that area.

When measuring L7630 in continuity mode, while on the board, i get a beep and a reading of 004 from my multimeter. While removed from the board and measuring in ohms it shows 0.2-0.5ohm resistance.

Furthermore, the capacitors C1270, C1271, C1275 and C1276 while in continuity mode measuring between the ground plane and both sides of the capacitors, i get a beep and a reading of 004-005 on my multimeter and measuring in ohms between the ground plane and the caps I get 0.6-0.8Ohms on the ground side (pin 2) and 0.6-1.2ohms on the cpu side (pin 1).

edit: upon removing those 4 capacitors I found that measuring continuity between groundplace and pin 1 of the 4 caps no longer give a beep and give a measurement of ~175 and when measuring ohms between pins 1 of the 4 caps and the ground plane I get ~190 ohms. But between pin 1 of each of the 4 caps and pin 2 of L7630 I get a beep and a measurement of 4 in continuity mode and measuring ohms between those pins I get ~1.5 ohms. While in the boardview I see no direct connection between pin 1 of those 4 caps and pin 2 of L7630. (R7640 is not present.)

edit 2: One of the 4 capacitors measures as a dead short, unfortunately don't remember what position it was on. (I had the caps in order of removal on my bench but a draft blew a sheet of paper right along where I had placed them, mixing them up. >_< )

Do you think replacing the shorted capacitor and corroded inductor would fix the problem or might there be something else damaged?