MagSafe is Stable Green/Amber but system is not switching on

I have a 2013 13” MacBook Pro (A1502). I was using it normally with no distress for a long time.

One day it refused to switch on in the morning (no damage of any sort). The MagSafe charger is stays stable at Green (and sometimes Amber). I have tried:

• Leaving it on charge for a long time
• Reset both SMC & NVRAM
• The MagSafe light switches from Green to Amber and back to Green when doing the SMC Reset
• Long pressing the power button
• Disconnecting Battery, connecting MagSafe and long pressing the power button

The fan does not switch on; the laptop looks like a brick at all times - the only sign of life is the MagSafe charger.

Please help!!

Edit: Corrected a typo: Its a 2013 model MBP not a 2015.