Dell Studio 1749 :: Shuts Down Randomly Without Warning And Then Won't Start Back Up

I'll be using the computer and all of the sudden it turns off, it doesn't log off or say it's shutting down, I mean it literally loses all power. Then I try to restart the computer and you can hear the machine start to come on but then it dies again. I've tried charging it, I took the battery out and put it back in, etc. I'm just not sure what the problem is. I've only had the laptop for 1 year and 3 months and a few weeks before the year warranty expired the computer started to say that the battery life was coming to an end and so Dell had to send me a replacement battery. I've tried leaving the computer alone for days at a time and still nothing and of course it's no longer under warranty so I can't even call Dell without getting charged.