MacBook Pro Retina Battery Issue

I use a Macbook Pro Retina Late 2013 model. It hasn't been used much and the cycle count is just 38. It is out of the 1 year warrantee coverage by Apple.

One day suddenly, I shut down the Mac and when I tried to switch it on, Mac won't switch on without connecting the charger.

Now the charger condition is showing as Replace Now and I don't understand what else to do. It is almost a brand new battery and I am hoping for some replacement from Apple even though the warrantee is not applicable.