Is my laptop dying?

My PC's too old and I'm trying to save money to buy another one. I got a laptop which fan is broken. I think it doesn't work anymore. I think so because when I do too much stuff with my PC it gets too hot and then the screen turns black until the computer shuts down on its own. Happened to me many times... show more My PC's too old and I'm trying to save money to buy another one. I got a laptop which fan is broken. I think it doesn't work anymore. I think so because when I do too much stuff with my PC it gets too hot and then the screen turns black until the computer shuts down on its own. Happened to me many times but it's still working though. The battery's dead also, doesn't work anymore. I use the laptop only with charger but the battery is removed. Am I doing anything bad to it? I'm trying to use as little of it as possible so that it doesn't get hot. All my files are in there and I don't want it to break irreversibly. Are there some advice?
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