If it fell could a huge number of things, memory loose, something on the motherboard broken, could be the power supply also, or the battery. Try starting it without the battery, if that works, just get a new battery.
Can also try a new power supply. Although with the info you provided, it's probably some internal damage. A small stress with heating/cooling and moving the laptop can easily end up being a crack or full damage after time.
Unless it's a very new laptop, you are better off buying a new one than trying to repair it.