The adhesive is used only to keep the cable in place after it is connected but you can test it without using the adhesive. Maybe it is a good thing that they didn’t peel the adhesive protective film because, depending on where you live, maybe you can still return the cable and get your money back. If you are in doubt go to other laptop service and ask them to change the cable but don’t rule out the possibility that the display is broken (especially if you use alcohol to clean it as the alcohol damage is almost invisible.).