[Spartarus]

Let me make a wild guess...

This happens when you get in, turn the key from full off, all the way to start immediately without pausing. Nothing happens. Release to "ON" and try again, and it fires up immediately...

If I am correct, then I had your exact same problem, except on an MT car.

I've looked over the starting circuit thoroughly, and all I can say is either you have a sticky relay or a bad battery. Here's the justification.

Unfortunately, on this car, the ground path for the start relay doesn't go straight to the battery, it vanishes into the ECM at pin 26, and then goes god-knows-where. We like to call ECU's "logic boxes" in my field... And they make troubleshooting a ROYAL B*TCH.

Either way, there is undoubtedly start logic in the ECM that controls this ground. if you close the contacts for the two start switches in the key switch before all the other relays close and everything is powered, nothing happens. There is start-inhibiting logic somewhere in the ECU... Pity there's no documentation of any kind... Sigh, logic boxes.

All it took to solve my problem was pausing a half-second at "ON" before turning the key all the way to "Start"... But it was irritating, because I didn't have to do that when the car was new. Charging the battery made the problem go away for a while, and I didn't want to start chasing relays.

Anyway, If your battery is older, and the charge retention has gotten worse, and the cold start voltage is down, it may not have the initial "kick" to close all the relays in the fraction of a second that it takes you to rotate the key all the way from off to start.

In older cars, it didn't matter, because the key switch went straight to ground, but in this car it doesn't...

For example, on an old MT car, if you turn the key to "START" first, and then depress the clutch, as soon as the clutch bottoms out the engine will crank, because the clutch switch completes the starting circuit. BUT on the FRS, you do the same thing, and nothing happens. Start is inhibited by the ECU because it wasn't in a "ready" condition when the key closed the "Start" switches.

On your car, you have no clutch switch, you have a neutral inhibitor relay in the AT shifter which completes the same logic circuit, but it's the same concept.

The TL : DR here is it's going to be hard or impossible to determine exactly what the problem is. Try charging your battery and see what happens.