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I have a Handa Accord 1999 that won’t start on cold days but starts fine on warm days. It cranks fine and the engine turns over great but on cool days (or in the cool of morning) I have to crank it on and off for about three minutes. I can hear the buzz of the fuel pump when I turn the key but there is not even a sputter for the first two minutes. I also put a code reader on it and it didn’t find anything wrong with it. Why does it only start well on warm days or after it has been running for a little while?
I don’t know exactly how the Accord fuel injection system works, but from your description it seems the mixture air/fuel is not enriched properly due to some malfunctioning part. In cold days the mixture percentage gets more fuel saturated for the first few minutes until the engine reaches a target temperature..that seems not to happen in your car, hence the troubles in starting up. Your attempts to start up the car increase engine temperature until it can start ignition. It doesn’t seem a difficult or particularly expensive repair.