Hi my name is John from www.***
Inside all laptop batteries is a small computer that manages battery charging and monitors the safety of battery looking for conditions that could cause a fire. If your VGP-BPS24 is blinking one amber indicator light that means the battery has detected a "not safe to charge" condition and its best to heed that warning and just replace the battery with a new one
It may be possible that your battery is still under warranty from Sony but I think 1 year is all they offer for batteries.
Hope this helps