If you don't have those systems working and all components, I'd remove it all and restore the stock parts to be more secure from shorting or damage. It might be harder and still not free to repair or get those things to operate again, plus it could take as much time as buying new systems etc. The exposed wire was most likely taped over, but tape lets go. The main ignition wires are the big ones to worry about, you don't want any of them to be damaged. A short could fry a section of a wire, and that can be a huge problem to trace and repair. So prioritize the main wires, those are precious and you don't want to ever have to mess with them. If your key code works by moving it nearer to the PATS receiver, that's great, you shouldn't have to deal with dealer programming(still if you have two good keys). The PATS module stores the key codes in it, the rest of the components you can replace as needed.