Laptop won't boot

Ok I see a lot of questions about notebooks that won't boot. Is this a fluke or is there a good reason? My hp pavilion has the prob...black screen...blue lights on Function keys turn on as long as I hold the on button down...that's it....nothing else. I tried various suggestions .... disconnect battery...hold upside down. Shake. Etc. No luck. My battery has been dead for months will not charge computer won't start with battery out or in difference. WHat next??