If the LED or the light indicator is blinking, then something is going on with the battery. It could be hardware but we cannot tell right away. Please follow the steps here to isolate your issue:
Check the battery health on Vaio Care (Desktop) - If indicated as "critical" then it already hardware issue
Power cycle - Remove the battery and all peripherals -> press and hold the power button for 5 seconds OR, if the battery is not removable, remove all peripherals-> look for a battery off button on the bottom of the laptop -> push the button for 5 seconds -> you may use a safety pin if you see a pinhole.
Reset BIOS - Turn off the unit -> press and power button and immediately, keep hitting F2 key. Once in BIOS, go to Exit tab -> Get Default Values -> hit Enter -> Save changes and exit.
Download or update Sony® Shared Library, Sony® Firmware Extension Parser Device Driver, BIOS Update Utility from Sony's website based on your location or from where you purchase the laptop.
Your Vaio VPCYB15AG is an Asia-Pacific model and we have limited information about your unit.