My laptop E5-521-20AP won't Power On

Hello everybody,

To begin, I'm sorry for my English, it's not very good because I"m French.

I have the Acer Aspire E5-521-20AP and my laptop won't power on with the AC Adapter, he works only with the battery.
When I plug the AC Adapter when the battery is in the computer I have the Orange LED indicator turned on, he tells that the battery is in charge, and Windows tells me the same, but in reality my battery is discharging.

I think it is not a problem with my AC Adapter, because he work fine with another computer.

To conclude :
1. Only AC Adapater --> Don't won't to Power On, when I press on Power Button, nothing  happens

2. Only Battery --> Computer Turns On, all is OK
3. AC Adapter + Battery --> Computer Powers On, indicates that the battery is in charge, but in reality, the battery is discharging.

My computer is now not under Warranty, can somebody give me the service guide to repair it please ?
I think it is a problem with the Power supply circuit of the computer

I wait for your replies, and I hope to see my computer working...

Thanks in advance,

Anton.