when you say "40-50 minutes and then it getting on", do you mean that the laptop boots up fine but the monitor doesn't turn on till 40 minutes after? I'm guessing the computer is already at the desktop or login screen when the monitor finally turns on?
I have seen some monitors do this. It is caused by bad monitor capacitors. (screen wont power on for a good 20 minutes after turning it on). I probably just needs a new monitor or send it to Acer for warranty repair.