Black screen the battery is dead, so i usually plug it directly... 2 days ago when i powered on i could see faintly windows was runing behind the dark screen

From what it sounds like, you are looking at replacing one of two things. inside your screen is a backlight. depending on what type, (chemical tube or led, more often then not its a chemical tube they go quickly) number two item is your inverter. the inverter supplies the power to your backlight, usually located under the screen, attached to the metal frame of the screen(you have to remove the plastic framing) in other cases your inverter will be integrated into the motherboard, or it will be plugged into the motherboard. if its integrated, buy a new laptop as the motherboard will almost cost the same as the laptop. unless you want to risk damaging the screen to try and replace the backlight, i would go ahead and suggest looking up ebay for a inverter for your screen. you have no battery but you are plugged in directly. with this case i want to say its the inverter. but you need to know if its A) under the screen B) integrated C) on the mobo but not integrated. with A) you have a good chance of easily replacing it. with B) buy a new laptop. with C) you have to remove the faceplate with your plastic power button stuff and leds above the keyboard to access the keyboard screws. remove the keyboard and the inverter will be on the top left of the motherboard.