acer aspire 5740g strange problem

I received from my friend this laptop to take a closer look.. According to my friend laptop was working fine one night and in the morning it just wouldnt start again, nothing...
When i put in on the charger the 3 pwr led are up and blue, so everything ready to turn it on, but when i press power button nothing! No sound, no nothing.. I take it a part, clean the cpu cooler, replaced termal paste, replaced ram with the new one, put it together and again 3 pwr led are up, but when i press power button nothing happens, not even a sound.
Later that afternoon i tried one more time to turn it on and now acer was up and running But i really didnt do anything new in the meantime... so i left it to work a few hours and all was fine, i turn it off later, then in the morning turn it on and everything was fine. After a few days i was just thinking to call my friend to pick it up, but when i tried to power it one more time ... again no response.. again laptop wont power up, no sound at all!!!
Now it is almost one month in my flat, its like working 3 days, then 1 day it doesnt then it works 4 hours then 3 day it will not turn, then it works 7 days then it will not start a day.. you get my point...
I can not figure what could be the problem? Anyone have any idea? Charger is not original it is from bigger acer but same Voltage. Maybe the power connector on motherboard, but i dont see any loose or corrosion on it...What would prevent laptop from powering if the power leds are up and he is receiving electricity? Bed CPU?

Thank you in advance!