Alright, after an about 24hour charge (started charging it yesterday in the early afternoon), the charging LED is now turned off. I tried unplugging the Kindle and reboot it. No success, same thing as yesterday. After this attempt, I plugged back the Kindle to the charging cable.
It started to charge again, like the battery was completely empty.
I think the battery is gone and preventing from resetting the Kindle. I will try buying a new battery, and see how it goes. I'll keep you guys updated, so that if any others have the same problem as I do, they'll know what to do.