Dell Inpiron 8200 Doesn't Start

Hello,
My inspiron 8200 is not turning on. Nothing happen when I press the start button: no power on lights, no fans.
The battery is charged (I have an extenal charger) and the test shows it. The start button seems to be the problem. In the past, I was able to start the computer when the battery was charged. The computer, however, had some problem that prevented it from starting if the power cord was plugged in. So I had to remove the power cord before starting the computer and plugged it in once the computer was turned on.

What could I do to solve the problem?

Thanks,

Bhagwan Samyal