My 1997 Dodge Intrepid died while driving anout 25 MPH. It wasn’t getting a spark to the coil so I replaced some sensor the delivers the spark to the coil. Still wouldn’t start. My mechanic told me my timing belt and water pump where bad. He replaced both and after getting it home it wouldn’t start with out spraying a little ether into the intake. Then it would start but run extreamly rough until I could finessing the gas peddle until I got it above 5000 RPM then it would idle fine and purr like a kitten. I could shut it off and restart it as many times as I wanted the rest of the day. But the very next morning I would have to do the ether and gas peddle finessing all over again. At first I chalked this up to very cold starts. This would go on every day and each day it would take just a little bit more finessing until finally it wont start at all. My mechanic was stumpted. I have since replaced the coil, checked that the spark plugs are connected in the correct firing sequence. I have tested my spark plug wires and plugs. Now a couple of relevent or non-relevant side notes. You decide. Back in the days that I could actually get it to start. I would be going through the steps of trying to start. It would crank, and I would get what I can only describe as a back fire out of the intake occasionally. Also before I would ever spray the ether I would try starting it normally a few times and without stepping on the gas peddle I would get a very strong smell of gasoline in and out of the car.
This sounds very similar to a cold start on an old “choke” equipped car with the choke open. A cold motor needs an extra rich mixture of gas and air to start. Something in your fuel injection system that provides the extra fuel for a cold start isn’t doing its job. That could be a sensor or a connection to a sensor not getting the right info to the computer controlling the fuel injection.