Sony Vaio VPC-EB290X Rare Green Laptop MODEL PCG-71212L NEEDS REPAIRED

Sony Vaio VPC-EB290X Rare Green Laptop MODEL PCG-71212L NEEDS REPAIRED

Beautiful laptop I owned since 2010. Used for a few years before the screen went black. I took it apart and applied new thermal paste as it was running at a high rate. I was going to purchase a new screen, but never did, as I cannot determine if that would be the actual problem or not. I had all my info on the HDD so the hard drive is pulled/not included. May be an easy fix that I don''t know of??
If you can figure out the problem and get it working, hope you can. It has been put away for years, but includes all original box and pieces, manual, charger etc.