How do I fix my HP laptop? The screen shuts off.?

I have an HP laptop that I bought in 2009. What happens is that every time I turn it on is that the screen shuts off. It might work for a few minutes but eventually to screen goes black, but the computer itself is still on though. I believe the cause was on my return flight from Europe. I put my lap top in my back pack without additional protection, intending for it to be my carry on. Then the lady at check in advised that I should check in my back pack to go through security faster, because the security are Charles de Gaulle airport were on strike, and they would check it in for free. I went with it because I haven't been home for over four months and I was coming home for Christmas, I was tired and not thinking clearly, and I heard that the strike has made many people miss their flights without a refund, all because it took forever to get through security. So I went along with it. Since I got back that is when I have had this problem with my computer. I suspect this is the reason because I noticed a crack on the bottom side of the computer's shell, so perhaps my bag was knocked around too harshly when it was loaded on and off my flights.

What do you think the problem is? Is it worth getting it fixed? Would having it repaired be costly? If I do get it repaired where should I go to do so, that is is there a recommended business I should try, or should I mail it to HP?

Thanks everyone.