Why does my laptop only turns on with charger?

The issue is this: I power up my laptop (charger disconnected) and it turns on and shows the Acer logo for about 3 seconds and the fans turns on as well and then the whole computer turns off.
Only when I plug the charger for about 15 seconds and then power on the laptop, it turns on completely and works fine, it is on time and everything well like nothing ever happened and I can even "unplug" the charger after that and it still works fine without it and the battery lasting what it should last.
The battery is new, I bought a new one, and the problem still persist. The battery charges correctly as well.
My BIOS is updated.
Note: if the charger is plugged and I try to power on the laptop ****before**** the 15 seconds have passed, the computer turns on and sometimes goes all the way until the lock screen but then it turns off again. And after that I have to disconnect the charger completely from the laptop and also the power outlet, and then connect it all back again so the charger light in the laptop turns on and I can try to power it on again, but this time after waiting about 15 seconds so it can work completely fine.

Very weird.
Please help!