My desk is littered with the remains of at least seven Acer N35's.
The problem you describe is similar to having left it for ages with no charge. By holding down the power on button and gently wiggling the connecting cable you may find it will start to charge ok. This usually takes 5 - 10 times or more before you get the knack, however caution should be used as the connection piece is not as robust as is once was and can break off inside.
Of the seven I have; 4 have broken connectors just from normal charging, One - after a full charge - the back light refuses to work. One had a new battery inserted and will not go back together. One the power switch wheel on the top left has sunk within the unit and can't be powered on.
Shame really when the build quality was better they worked a treat, now they are a liability.
Rockman
December 2007