There is the possibility that when you first fired it up, that you didn't completely shut it down, in which case, the battery power has been depleted.
It's generally a good idea to charge the battery to a minimum 85% before the MacBook will fire up without the charger.
There's also the possibility that the battery has been completely drained.
Next time you power up with the charger, go into 'About this Mac' from the dropdown below the Apple logo.
Go to System Report>Power to see Battery Health. This will tell you the general condition of your battery and whether it needs to be replaced.
[Edited by Moderator]