Hehe, I love all these answers.
Yes, Ian, just solder that wire back to where it broke, and I can almost guarantee it will work just fine again. The car will default to controller ID 1, so try that controller first. If that doesn't work, follow the manuals for setting the car ID. If you tell us exactly which model you have, and what version it shows (if it's a 6 car base) when it first turns on, we can help.