@magicjet_
More information is needed.
What is the model number of the laptop?
What light is on? Assuming it is the power light only then if there is no image on an external monitor after you think that the laptop has "booted" when you have pressed the appropriate function key(s) to switch to an external display you have no way of knowing whether the laptop has booted or not.
You said that the screen is cracked but are there any images/backlights showing at all as cracked mightn't mean totally dead?
Have you tried to get in to the BIOS menu area on startup and check if there is a display of any kind, you didn’t say?
Have you tried a power refresh in case BIOS is corrupted and preventing a normal start? Here’s how to do this:
Disconnect charger if connected, remove main battery, remove RTC battery from motherboard (if it has one - don’t know the model so can’t help with this), press and hold laptop’s power button for 30 seconds then release. Reinsert RTC battery, reinsert main battery, connect charger and switch on laptop and check what happens.
If there is still no display of any kind when initially trying to access BIOS on startup then as a DIY repair all you can do is to temporarily replace the laptop's LCD display to initially check what is happening. It may be that the laptop is not even passing POST