My laptop won't turn on

I have an Inspiron n4010. I was working on it this afternoon, and it just turned off. I haven't been able to get it back on, and none of the front lights are on, even though it's supposed to be charging. The only time I get a light is when I first put the charger cord in, the rightmost light will flicker. I have tried taking the battery out and while not charging and holding the power down for 30 seconds. Nothing. Any suggestions?