HP Laptop screen very poor visibility n sometimes black

Hello, I have the same problem sort of. Sometimes when I hit the power button to turn my HP laptop G60 on the screen would come on for about like 10 seconds and then it seems like the screen would glitch and becomes a black screen or very poor visibility of like 2% visible. I have tried taking the battery out n holding the power button for 30 - 60 secs but that trick failed. I have hooked my laptop to a external monitor and the screen shows up on the external monitor. My battery is completely dead, my laptop have been running with the charger plugged into the laptop and electric socket for quite sometime now. I saw one answer on the forum about a back light fault, and was wondering how much would that cost to replace and be installed by professionals?