Sony Vaio won't start up and keyboard isn't responding

I own a Sony Vaio SVE14112FXB. This is not the first time this has happened. My laptop used to not wake from sleep mode until I took out the battery for a few minutes and then put it back in. After a few days of that, I disabled sleep mode and shut my laptop down when I was done using it.

Now my laptop won't start. I've done the trick with the battery and it isn't working. The backlit keyboard doesn't light up and the laptop doesn't respond when I press F8. It also doesn't respond when I press the VAIO button. I just bought this laptop in August 2012. What do I do?