All joking aside, if a laptop won't start up with the charger attached then the typical diagnostics are:
1) Remove the battery, use the charger alone. Try to start it. If it doesn't, continue.
2) Remove the charger and battery. Hold the power button for 60 seconds. This may help reset some electronic components. Then attach the charger by itself and try turning it on. If this doesn't work, continue.
3) Repeat step 2 except instead of plugging in the charger after holding the power button, install the battery by itself.
You may need to repeat steps 2 and 3 more than once.
It's also possible your battery is empty and the charging port is no longer working. In this case your battery is fine and your charger is fine, it's just...