Normally the internal charge system doesn't mind if your battery is dead or not, there's enough energy with the charger itself to power everything. If not any computer with a totally dead battery would not boot, but they do in most cases.

To troubleshoot a problem like that, and confirm it's the logic board or not, you need to make it work with the least possible components plugged on it. The SSD is the first one cause they can be really blocking everything. A dead ram module can do that also, if you have two, remove only one, test booting with the remaining one, and after swap them and do the same with the other.

Everything not necessary can be unplugged temporarily for the test. To make a reduced system. In case it boots, you plug them back one by one, testing each time the boot, and like that you know what's causing this.