That white wire with 4 pins (holes) is the programming lead, where you program the speed limit. If you'd shown that in the beginning, it would have saved some time.
Your LED panel carries battery voltage on some wires. If you shorted one of those to anything else in it, serious damage can happen, so it's probably finished now and would need to be replaced by exactly the same type, which I guess you'll only get from the original bike supplier.
You have one more choice, and that's to replace the controller and Panel with different ones, like a S06S and S-LCD3 from BMSBattery, though there's several complications:
All the connectors will need to be replaced (cut and solder wires)
Your present controller is wired directly to the battery connector, so you'd need to unsolder it and figure out which pins are the positive and negative. You can look in the battery to see which pins have wires on.
You need to find a place to install the new controller. I'd use a small tool-bag, like those that fit under the saddle or in the frame triangle.