shutdown when power charger is unplugged, turns on automatically if plugged

My 2,5 years old laptop, an ASUS N580GD, is suddendly showing a common trouble of ASUS laptops, but not only ASUS ones.

I read many people faced these troubles but I’m not finding a solution.

1) sudden shutdown on laptop when power charger is unplugged. A “Restore AC Power Loss” or "Wake on AC" or "Power on AC is not available in UEFI

2) when I put the power plug in , the laptop turns on automatically and without pressing the power button

3) battery is available but not charging (now it’s at 69% and I was able to update UEFI because system detects it)

4) I bought a new battery, but the laptop behaves as with the old battery. It’s NOT a battery fault.

5) If the power charger is not plugged, pressing the power button doesn’t turn on the laptop, in spite of battery at 69%.

6) With power charger plugged, charging led is fixed orange

7) MyAsus app detects NO problems

8) At Windows 10 startup, battery icon shows the charging animation of bars: after 20 seconds it stops. I suppose it’s charging for these 20 seconds!

9) I asked for support and they suggested me to follow https://www.asus.com/us/support/FAQ/1012793/ without success

Again: I bought a new original Asus battery and I have the same problems. It’s not a battery fault

I suppose this happened after a software update but I didn’t get which one.

Please somebody could help me to solve this!

 

Interesting news: the battery is at 70% now. I suppose it's charging in the first 20 seconds at start! I think it's not a hardware problem!
Does anybody know where to find Restore AC Power Loss on Asus UEFI?