I can't start it when it's cold!!!!

It was 20 degrees outside and 2005 Copper S (standard transmission) would NOT start. I took it to the dealership and they replaced the fuel pump. They said the starter/spark plugs/ignition/battery, etc. were all good and that without a doubt, the issue was the fuel pump.

So, I was feeling optimistic about the cold start issue being done for since I took the dealership's advice and got the new fuel pump. Except this morning the car was in neutral and I turned the key and cranked it. It wouldn't turn over. I cranked it again and held it for 5 seconds. The engine did not turn over. And I turned the key AGAIN and tried to start it for five more seconds. It wouldn't start! The weird thing is, the WHOLE time I had it in neutral with my foot on the clutch.

But then I tried starting it in first gear with my foot on the clutch and voila, it fired up IMMEDIATELY!!! My dad said that maybe the neutral switch is bad??????? But I thought that standard transmissions don't have a neutral switch??

Does anyone have any experience with this problem? It's becoming difficult to diagnose and I'd like to pinpoint it.

 

Yep, there is a switch on the clutch master cylinder at least on my non-S. I think it prevents starting.