Battery only charges while computer is powered on. If off, L shaped charger light stays green?

The L shaped charger led lights when connected to the laptop. If the computer is powered off, it turns green, but never turns orange (ie, charges the battery). Once I turn the computer on, the light turns orange and starts charging.

This means that I can charge the battery only if the computer is either on or sleeping, but not if the computer is powered off.

I'm afraid that if sometime I completely run off battery power, it won't be able to turn on if this behaviour still reproduces.

Any clue?

Thanks!!!