Welcome to the club giancarloboggian. I have the same problem. I bought a new battery. That didn't help. I have an Aspire 1 10 ' screen netbook. It's from 2005 so I guess I got my moneys worth out of it. Its heading for the recycle bin.
I have an Aspire 1 10.1 " screen. The yellow light is on, but it wont power up with the power switch. I just installed a new battery. That didn't help. Any suggestions would be appreciated. Thank you.