My laptop is not turn on at all. Even with power connected

If you have an Intel Mac, then try an SMC Reset.

Here are two Apple articles for troubleshooting charger issues depending on whether you have an older laptop with a Magsafe charger or whether you have a newer laptop with USB-C ports:

Apple Portables: Troubleshooting MagSafe adapters - Apple Support

If your USB-C power adapter isn't charging your Mac notebook - Apple Support

Try unplugging the charger from the electrical outlet for a minute to reset the charger's internal circuitry. Also make sure to plug the charger into a different electrical outlet in case the one you are using is bad.

Without knowing the specific model of the laptop, this is the only suggestions I can offer so if they don't help, then have Apple or an Apple Authorized Service Provider examine the laptop to provide you with a repair estimate.