ALWAYS use a plastic pry tool to disconnect those cables. You can use one to help you reconnect them too if you've got fat fingers like me.
That being said, modern computer grade laptops are absolute sh*t. When I get a computer in that's going to be expensive to fix (like, in your case, the screen needs to be replaced), I try to get my client out of here with a business class laptop instead. You could have gotten them out of there with an HP Elitebook x360 G2 or even a G3 for the same price as the screen on that piece of crap laptop.
I always tell my clients what garbage their computers are (assuming it's true, of course) and make sure they realize that the chances of me damaging something is quite high because the build quality is so bad on these modern consumer grade laptops. If they want to move forward with an expensive repair on a piece of junk laptop, that's their choice, but I want to make sure they make an informed decision.