Sounds like either a faulty power supply or a faulty motherboard to me. Since it's a laptop, there's not a whole lot you can do about it. One thing you can try is making sure that the battery is getting a clean connection, since it's a laptop. Just check to make sure there's no hair or dust or anything like that either in the battery slot or on the battery's connnectors.
Other than that, you can try to take it to somebody to see if they can find something out, but sometimes even if you have the computer open and are looking at it you can't be sure what's happening.
What I can tell you is that I had a desktop that was doing the same thing. I thought "Hmm, either this power supply or this motherboard are about to die" about a month or so later, they both died.