MacBook Pro Retina 15'' Late 2013 Stoppped Charging Related questions here and here.

Hi everyone. This is what happened to me:

I was giving a class, in a 200 people auditorium, and there were lots of power extensions and cables for everyone to connect their laptops while the class. I was running out of battery (about 20%) so I decided to plug my MBP to one of those connectors. I didn't notice if it started charging or not, I just trusted it would. Then after 20 min aprox, we had an hour off the auditorium, and when we got back, I connected the machine again, but this time I noticed the light in the charger didn't work. I thought it was an issue with the power, I changed the place but the MBP was not receiving any power.

I asked to my students for a different charger (thinking it was a charger issue) but trying 2 different ones, still light didn't turned on, so I thought it was an internal hardware issue. (at this point the MBP was still on, with 5% battery or so).

After class, I took the MBP to an official Apple Service center, they told me it was the "Magsafe" (like an internal little board that allows power from charger to battery?) and the charger, both of them seemed to be damaged. Most likely an overpower incident. I understood since it made sense.

Now issue is they asked warranty Magsafe piece, the installed it but machine still not turning on. THey say at Apple Service retailer that could be Logic Board, but does that even make sense? Could a MBP still be on and working if logic board is damaged? I mean, the machine never got turned off, it was alive until battery drained out...

Now we are waiting another freaking 4-5 days to get the logic board. I'm getting crazy since that machine is my main work tool. What do you guys think it could be?

EDIT

Now, I get that this specific model's parts are all welded, so, a new logic board would mean what other new pieces? I'm worried about the data in my hard drive.
It is possible the logic board needs to be replaced. 

I would try resetting your SMC (manages the power in the laptop):


Shut down the computer.
Plug in the MagSafe power adapter to a power source, connecting it to the Mac if its not already connected.
On the built-in keyboard, press the (left side) Shift-Control-Option keys and the power button at the same time.
Release all the keys and the power button at the same time.
Press the power button to turn on the computer.


Note: The LED on the MagSafe power adapter may change states or temporarily turn off when you reset the SMC.

For the full Apple KB Article: https://support.apple.com/en-us/HT201295