Laptop screen is black when I try to turn on?

I have a Dell Latitude D830 laptop. Sometimes when I start it up, the screen won't turn on (black screen). The power light is on and the numb lock is on but the screen will not turn on. I've tried taking the battery out and holding the power button for 20 - 30 seconds then putting the battery back in etc. but it still won't turn on.

I find that my laptop won't start up if it is heated up so I'm thinking that something may have gotten over heated? Even when it isn't hot it still won't turn on. Right now it's working but it gets really annoying when I need to do an essay it just won't turn on. Even if I leave it for about an hour, sometimes it turns on and sometimes it doesn't.

I also find that when my laptop starts to get hot, really slows down. When I restart it, then it won't turn on.

My brother gave me this laptop for a present ( it was his for about 4 years ) and I'm trying to fix it before he finds out about it. I don't want him to get upset. Please help!

~ Thanks. <3