Just had the same issue with someone’s 2012 13” rMBP. However, it just started doing it by itself. Was never disassembled. Charger glowed orange, and I was able to power on if I held down the power button while plugging in the charger, although it ran with fans on full speed, and battery wasn’t recognized.
Checked out the battery and connectors physically, but it looked good, apart from some dust. No swelling or the like. Pressing the power button alone would spin the fans in slow bursts, but nothing else.
Tried SMC and PRAM resets multiple times, didn’t work. Then I tried plugging in the 85w charger from my own 2013 15”, and it turned on instantly, battery recognized too. It was on zero percent charge though, but started charging normally after a few minutes. Maybe the battery was so drained that the smaller charger couldn’t kick it into life - it does have lithium batteries, and this can also happen on 18v power tools lithium batteries, where you have to do a few things before they will charge, if they are completely drained. Normally a Mac will shut down by itself before they drain completely, but I’m not sure what happened in this case. Works now though, also with the smaller charger.