The most common issue with a laptop that will not start up is a faulty power supply.
If you are using a replacement charger, make sure that it is the correct one for your laptop.
Try another charger which is known to work on another device.
Check the screen
Try disconnecting external displays such as monitors, projectors, and televisions.
If you see power LED lights and can hear the laptop making sounds, try turning off the lights in the room to see if there is a faint image appearing on the screen. Sometimes LCD screens go out and need to be replaced.
Remove any USB drives, CDs/DVDs, or memory cards
Sometimes the operating system can get stuck before loading Windows, media such as USB drives, CDs/DVDs, or memory cards can be the issue.
If your computer is trying to turn on and you can hear it, you may be able to enter Windows in Safe Mode, this mode will allow you to undo any changes that made previously that is causing the start up error.
Press F8 as your laptop is starting up and you will see a menu allowing you to boot in Safe Mode.