Hello and welcome to Bleepingcomputer.
I have some very helpful links for you for your laptop which comes complete with photos to help you out.
This first link explains how to disassemble the laptop screen, there are two pages to this link, so look for the PAGE 2 link, below the google ads to proceed to the next page.
This link is the total disassembally of your laptop complete with photos.
Hope this helps.
Beyond your reconnecting that wire, if your laptop screen continues to remain dark, you may need a new backlight or inverter.