Chosen Solution
I’m struggling to figure out my GF’s Macbook issue. She had A1502 (Late 2013 Retina) and hardly uses it (occasional at home and music studio to play songs). One day it was used and carried back home but would not turn on anymore after return. After quick search, tried all the resets and then disconnected the battery. It was a changer as Macbook would boot with only charger connected and can boot once with battery connected but after shutdown, would not. Symptoms. Only works with charger connected, does charge the battery, but would not work with battery connected to MBCPU seems like under-clocked running on charger, loads everything super slow and thinks too muchI have tried to change the battery with iFixit kit, same issue, no change (anyone need spare battery?)Keyboard/touchpad works without flaw, all keys do work. The only other thing I can think off is the motherboard but not willing to invest more money into unnecessary parts, would like to figure out solution. Keyboard replacement?
Update (09/12/2019) FIXED: Keyboard was the culprit. Replaced with new OEM keyboard from eBay and all the problems disappeared. 3 hours to change though.
Here’s the iFixit guide to replace the battery MacBook Pro 13" Retina Display Late 2013 Battery Replacement and here’s the needed part MacBook Pro 13" Retina (Late 2013-Mid 2014) Battery