I really must make a sticky post about this. Here goes.
Laptops are made of just a few "parts." I can't write this over and over but will until I make the sticky post.
We have the power brick, display panel, main board, keyboard, drives, cables and the other tiny bits and that is what is changed out when you have a failure. Today, it's how these are fixed.
Your failure sounds like an intermittent connection or device on the mainboard. Price out a replacement mainboard. Acer is the source for the part.
When I press the power button on my laptop the green led lights and the fan starts and in 2 seconds it shuts off, and then starts doing the same pattern over and over.
When I push very hard just below the power button, the laptop starts until I take the pressure off. On the other side of where I push is the part in the motherboard that's the closest to the battery, so I suspect something that's responsible for the power.
Btw, it does not make any difference if I run the laptop on the AC or the Battery..
My laptop is acer aspire 7520.