Mid 2012 Macbook Air Not Powering On

A while back, my Macbook all of the sudden turned off. If I remember correctly, it was as I was pressing a key, but also could've been a coincidence. The laptop let off a burning smell and never powered up again. Now, Im revisiting this laptop to see if I breathe some life back in it. The mag safe charger is orange when plugged in, but the power adapter still feels cool. Holding control+shift+option+power turns the mag safe light green for a couple of seconds. I was thinking at first that it was a bad logic board, but the fact that the keyboard inputs are working makes me think that it could be a battery. Does anyone know how the magsafe light would behave based on a bad battery versus a bad logic board? I really want to get to the root of this issue and do not necessarily want to discuss if it is worth it for an old machine.