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If the plug in the camera you bought is broken, I advise taking it back for a return to the store or vendor, and an exchange for another fully working camera of that type.
If the receiver has a broken plug on it, I advise you to take it out (or have it taken out) of the car and serviced to replace that plug.
Nothing else will work so well for sure. (And I cannot hazard any instruction about repairing - or 'hot-wiring' that plug, without knowing something about the maker and model #, and which plug it is on the receiver, precisely.)
(A note: if the plug was so badly broken that it shorted out two of the plug's wires, it might well be best to have the receiver taken out and serviced, and then tested after the plug is replaced, in case the circuitry behind that plug was damaged by the crossed wire short. Another reason why I said, nothing else will work so well for sure.)