Laptop Screen Won't Turn On

Hello,

I have a Gateway laptop, and for quite a few months it had been having an overheating problem. It would turn on, work for a few minutes (usually around 15. 40 was the most I ever got out of it), then shut down. I'd then have to let it cool down and repeat the process. It got to the point where I'd just use it to get a file I needed transferred to another computer. Now, however, the screen refuses to turn on. I've tried everything I can think of to get it powered back on, but nothing's working. When I try to turn it on, power lights come on and the fans begin running, but the screen remains blank. I THINK the overheating and screen issue are somehow connected. If anybody knows how to fix these problems, let me know. I'd like to get it on at least one final time to transfer my remaining files to a portable hardrive....