I will give a quick tips on why a laptop does not display when power on. These are based my experiences fixing laptops like sony vaio, dell, asus and acer. Most of them I fixed with this kind of problem not displaying when turned on. Here are my solutions. I hope it helps.
Quick Fix - Laptop Not Displaying When Turned ON
Use external monitor for testing - try to use monitor and connect it to the vga port on your laptop, if it has display, then you have an lcd problem with your laptop. You can buy an lcd replacement for that model of your laptop online.
Check the memory sticks - most of the time this will surely fix this problem. Locate the memory card or sticks on your laptop and clean it with eraser or anything will surely cleans the copper. Please be cautious while cleaning.
Reheat GPU - sometimes graphic cards needs to be reheat. This is the best solution when there is no display on your laptop. GPU is not working well because of overheat. You can use equipment like heater or any electronic heater for this purpose. Remember to apply thermal paste on GPU after fixing to avoid overheating.
These are the only quick tips only I can give if you have problem with your laptop not displaying when turned on.