question re charger surface pro 6 - help with charger indicator light

Hi. My question is, when the power cord is plugged in and turned on, is the white led light  meant to be on if it is not connected to the surface? The led light is always on so i am hoping it is just the cord that is the issue. 

This is something I should have noticed when using it (surface pro 6) but I never paid attention. My surface suddenly stopped charging and I am trying to figure out if it is the power supply or the surface that is the issue before spending momey on another power cord. I can no longer turn it on as it is ompletely flat.