Won't turn on (except very rarely)

Hello everyone. I have a MacBook Air A1466 with a very strange behaviour. I've tried a lot of possible solutions I've found here but nothing works. The device is not mine and I only received it a couple of days ago, so past behaviour descriptions might not be as reliable. Here's the situation:

Apparently some time ago the device started having some issues when booting. At times it would simply not turn on, neither plugged nor unplugged. Trying again some time later it would turn on and then work perfectly for some time, botting and shutting down, etc, then randomly the issue would reappear. It was sent to 2 different repair shops, one changed the battery (not necessarily related, but it was due for a change anyway). Both didn't find anything, claiming it worked fine while they had it.

The problem started happening more often, until the owner decided to get a new macbook and they gave this one to me. The first time I tried to power it on, it booted fine, got to the lock screen, I entered the password and it started filling a bar, like it was upgrading something. Right before the end the computer shutdown, and it wouldn't turn on again. Since then I've managed to turn it on twice more with the exact same result (lock screen, entered password, bar filling, sudden shutdown). When plugged, charger turns green briefly then stays orange.

I've completely disassembled everything: removed battery, speakers, main board, I unplugged every connector to check for corrosion. Removed the trackpad too. The insides look pristine. I did find some really minor blemishes and just a tiny bit of oxide on the outside of a couple of the biggest resistors, but nothing on the board or paths.

When power button is pressed, sometimes the fan will spin for a bit then stop, other times it won't turn at all. Same when power is plugged in.

So far I've tried:

Unplugging and replugging the battery and power cord (like a thousand times each).

Cleaning the power socket.

Unplugging components and trying to boot up without them, one by one and in all combinations: SSD, speakers, track pad only, whole keyboard assembly, screen, cooler fan.

Checking wheter USB ports can charge something (they can't)

The shift+option+cmd+power combo to reset SMC. This appears to do something, as the led in the charger cable turns green for a moment when releaseing the keys, then turns back orange.

I really don't know what else to do. It's so odd that the machine is definitely not bricked as once in many many tries, it does turn on. Next time it does I'll try NOT entering the password, and just leaving it at the lockscreen to see if it'll stay on.

I haven't done any voltage testing as I wouldn't know what to test, but I do have equipment to do it if necessary.

Any help will be greately appreciated.

Quick update: I disassembled everything down to the main board and did a full visual (magnifying lens) inspection. I found tiny bits of grime and specks of dirt, but nothing relevant. During one of many test, the fan started spinning and it actually stayed on for quite some time (maybe 30 seconds or more). I tried that a few times and the same happened, so I started reassemblying everything, to see it the machine would boot, but about halfway done it stopped doing the fan spin when plugged.

I did some very basic voltage testing: when plugged in I do get 15V and 3.4V on the MagSafe connectorr (on the board side). There's also 8.5V on the big inductor accross the board, as it should be, and the fuse right next to it does have continuity.

Any suggestions or ideas of what to try next?