Won't start

That sounds like a cpu, ram or motherboard issue. The cpu could be bad or unseated, the ram could be bad or unseated and it could be anything on the board.

Gnerally the common thing that will cause it not to boot and not show any error or video etc will be ram. That is where I would start. You can try removing any modules or just trying one at a time or in a differant slot. Ram is cheap(ish) right now so it would be worth fixing if that is the cause. You can replace the cpu or swap it out. Replacing the motherboard requires it be stripped down and you may find a new motherboard for $150-$200 and then the labour on top. Better check for any warrenty if possible. And if you need to pay out of pocket consider getting a replacement laptop. New ones have dropped down enough that the repair cost could be as high as replacement.