A good way to test the keyboard would be to connect a USB keyboard and see if you can input information that way. If so, then the keyboard is most likely either broken/defective, or the drivers are out of date/not installed properly. This can be fixed by first reinstalling the drivers in Device Manager to see if that is the culprit, then replace your laptop's keyboard if not.
The most likely reasons for a laptop to not turn on, involve either a dead battery, or a defective charger. The charger and battery can be tested at the same time, where the laptop will turn on, regardless of a dead battery, if it's plugged into a working charger. If the battery indicator at the bottom states a refusal to charge, then the battery is most likely dead.