I can't open my laptop. I don't know what happened

So, I was using my lenovo laptop for a school project. In the middle of typing, it just died. The screen turned black. Power out. I was charging it when it turned off so there's no way it just ran out of battery charge. Anyway, the charger seems to work fine. It still lights up while the small lights (I don't know what they're called) of my laptop which indicates whether it's charging/on doesn't seem to light up when charged/plugged. I tried removing the battery and plugging the charger again but it didn't work. Could over-heat be the cause of the problem? I smelled the vents of my laptop after it died and it smelled kinda bad, like something burned. What can I do to make it work again without spending too much money on repair?