What is the history of the car? Were the symptoms sudden or is this a new purchase?

Pull the cold start injector off the manifold and look for leaks from the tip ( I'm pretty sure it has one ) . Also probe the electrical connector, the cold start is only used something like sub 40*F and only while cranking. This system should have a thermo time switch controlling this action, if the cranking event occurs for too long, the cold start injector is supposed to shut off.