The laptop is about 5 years old so may need a clean.
- First step is to see if the fans are clear of dust. This guide will show you how to open the case. Make sure the charger is unplugged before openning case. Blow any dust from the fans and any where else inside the case. Be careful to not touch anything unless you discharge the static electricity from your body.
- The heat paste on the CPU and GPU may need replacing.
- If it turns off when the charger is unplugged then the battery likely needs replacing.
Click here for replacing battery video
It also includes instructions on how to properly "condition" battery before normal use.
- Does the video still not work? Try connecting to an external monitor or your TV. Do you get anything on the TV/monitor screen? If yes then your laptop screen is either defective or the connector is not properly attached.
- If no then your GPU (graphics) is damaged from the heat.