My 2004 grand am has issues starting when it’s cold. It has a new battery, the starter has been tested and was good, and it is not throwing any security light. When I try to start it, the lights and everything come on like normal but it doesn’t start. It wont even try and it only happens when its below 45 outside.
I’d suggest the fuel pump is on its way out given the cars age and mileage… wait, you didn’t tell us the mileage, or the engine that is in it so this is just a guess on my part.
The best thing you can do is take it to a shop that can let it sit overnight and try to start it when it is cold with a scanner hooked up. It could be a bad temp sensor, or leaky injectors or a weak fuel pump and more. Pay the fee for the diagnosis to find the cause rather than guess and throw parts at it.
Try shifting the transmission into neutral and then see if it starts.