Yeah thats a strange one mate?! Must be some sort of wiring problem (er... obviously lol ). I'd take a look at the starter wiring first!
It starts without the cold start injector ok because your main injectors are probably leaking whilst the car is stood up and so there is plenty of fuel in there for a cold start (this is the most common reason for unpluging the cold start injector, when really the main injectors should be replaced!).