Knc1, thank you very much for your answer. I've managed to open the back cover of my k4 without damaging anything. As you said that removing the battery is very difficult without breaking the device, I've not touched it (I don't have other battery to replace it).
I unplugged the battery cable and took my multimeter to see if the battery gives any voltage. The battery gives near 3.8v, so it seems to be fine...
Any more ideas???