The plate is part of the EMI screening to prevent signal leakage as well as intrusion from other sources. It also helps in making a good physical connection of the contacts on the other side, basically its’ needed.
Why did you remove it? It’s well secured not likely to fall off on its own.
Well you have a bit of a mess ;-{
First the cable is not workable in its current state. You’ll need to replace it, here’s the needed part 13” Unibody MacBook/Pro LCD/LVDS Display Cable, Apple P/N 661-4820. Here’s the guide to replace it MacBook Pro 13" Unibody Mid 2009 Left Clutch Hinge Replacement
Your logic board connector is also to far gone, you’ll need to replace it too. Now the tough part do you have the soldering skills to do it. This connector is not easy! You need to either heat and keep the connectors solder joints wet or you need to carefully desolder each pin carefully one by one and then the ground base without lifting the traces. Here’s the needed connector LVDS Display Connector (30-pin)