I can hear the fan running, but my laptop won’t turn on

One day I went to power on my laptop and everything worked as usual (the LED lights indicating that the battery was full and power was on were on, and I could even hear the fan running), but the only thing is that is was taking longer than usual to actually turn on. The screen remained black and I sat by waiting for it to turn on for probably 30 minutes or so, but still nothing.
I’ve tried that thing where you remove the battery and the charger and hold the power button down, but it didn’t work. I have tried multiple times too, and I have yet to get any results from it.
Anyone know what the cause of the problem is, and if so, how do you fix it? I really need help...
Thank you.

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Clarification Request
Similar failure.

It was the motherboard so we shopped for a new laptop.

You left out the make, model and age. I could toss out that I'd try a new CMOS battery but I don't see the make, model and age to check if it's time.

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Well crap.

Yea I’m sorry I am completely clueless when it comes to computers, but mine is about 4 years old. Don’t know how to figure out the model or make though.
I was just wondering, if it is a problem with the motherboard, could you possibly get it fixed? Or is it more reasonable money wise to just buy a new laptop?

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Why not use Speccy?
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Clarification Request
Is this ONLY a screen problem?

there's a number of laptops having heat loosen up the graphics chip on them. Part of the reason for the problem is hot CPU causing a heat flow toward the graphics chip since they often share a heat tube between them. There are a multitude of videos on youtube concerning the problem. I'm not a fan of the " bake the laptop" fix, but it fixes some of them , for a while. Others use a heat gun to get the GPU to melt the lead enough to refasten it.

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