is the battery at 95-100%? some laptops do not charge the battery if it's almost full to avoid overcharging, it's a feature to prolong your battery life.
If the battery is at 50% and not charging then that would indicate a problem. as advised above, try removing it and reinserting again.
What does the windows indicator says when laptop is plugged in?
you have several options either LED broke and doesn't want to show that the battery is charging or there's a problem with circuitry and charging isn't possible