XPS 13 (9350) - Battery problem (blinking orange indicator)

Hello,

As of today my XPS 13 started to behave in a very strange way.
It only boots and works when it's plugged in to a charger, and it doesn't seem to charge the batter at all while it's plugged it, which is stuck at ~48%. When I plug it out, it power off immediately and I have to plug it back in to be able to boot up. Additionally to that, the light indicator below the touchpad is bliking rapidly with an amber light (~3-4 blinks per second).

Any ideas of what might go wrong ?